Burress, who accidentally shot himself Friday night in the right thigh at a Manhattan nightclub, did not enter a plea on the class C felony charges, though his attorney said Burress planned to plead not guilty.
Manhattan Criminal Court Judge Felicia Mennin ordered Burress to return March 31.
Defense lawyer Benjamin Brafman argued for no bail, saying: "He has 35 million reasons to come back to court" -- referring to Burress' $35 million contract with the Giants.
Prosecutors also released a criminal complaint that provides a witness account from the club where Burress shot himself, the Latin Quarter.
A witness reported hearing a popping sound before Burress' legs began to shake, according to a criminal complaint. It said the person saw a bloody pistol fall out of his pant leg and land on the floor before Burress said "Take me to a hospital."
A grand jury will hear evidence and make a decision on whether Burress will be indicted.
Illegal possession of a firearm carries a sentence of 3½ to 15 years in jail.
Police escorted Burress out of a midtown Manhattan police station in handcuffs earlier Monday, placing him in a car in which he was taken downtown for booking and his court appearance.
Burress arrived to the 17th Precinct station shortly after 8 a.m. ET in a black Cadillac Escalade wearing jeans and a black coat.
Burress had a concealed-weapon permit issued to him in Florida, but records show it expired in May and New York does not recognize out-of-state permits anyway, New York media have reported.
"He is standing tall. He is a mature adult," Brafman said. "I think any professional athlete in this situation would be concerned."
The episode set off a frenzy that showed no signs of letting up Monday: Police said the case could expand beyond Burress, with authorities investigating Giants linebacker Antonio Pierce and whether the hospital Burress checked into failed to report the shooting. The NFL is closely monitoring the developments as well.
According to the New York Post, the hospital, the New York-Presbyterian Hospital/Weill Cornell Medical Center, failed to report the gunshot as required by law after hospital personnel recognized Burress, despite his checking in under a fake name -- Harris Smith.
He also told the hospital he'd been shot at an Applebee's restaurant, the Post reported, citing unnamed sources.
A more detailed timeline of the evening also emerged. Police have looked at security video from the club and hospital and determined that Burress arrived at 1:20 a.m. and left at 1:50 a.m. He arrived at the hospital at 2:04 a.m. and went home 11 hours later.
Originally, police had said Giants running back Derrick Ward was with Burress, Pierce and two other people at the club, relying on information given to them from security guards at the bar.
But Ward's agent, Peter Schaffer, said Ward is no longer a person of interest to the NYPD, the Star-Ledger of Newark, N.J. reported.
Schaffer said Ward told police he was at a Thanksgiving weekend charity event in New York earlier Friday night. Schaffer said police checked out the alibi -- inlcuding video surveillance footage of the event -- and agreed Ward was not with Burress at the time of the accidental shooting, the Star-Ledger reported. An NYPD spokesman declined comment on the report.
Ward said he wasn't with Burress on Friday night, and learned of the shooting on Saturday along with other teammates. He said the last time he saw Burress was "that afternoon [Friday], right after practice."
Asked if he would say where he was Friday night, Ward said: "It doesn't really matter where I was. It just matters that I wasn't with them."
Burress had been allowed to bypass security, even though they knew he was armed, according to a law enforcement official who spoke with The Associated Press on condition of anonymity. The club is said to be fully cooperating in the investigation.
At some point, as Burress was being escorted to a VIP area with a drink in one hand, he somehow ended up fumbling his gun -- .40-caliber Glock -- and it discharged, hitting his thigh. Pierce was with him when that occurred, police said.
Police said they had to track Burress down by canvassing local hospitals, and he had been discharged from New York-Presbyterian by the time detectives got there Saturday. An administrator then refused to give detectives information, citing privacy rules, police said.
Pierce was interviewed by NFL security at the Giants' hotel Saturday in Washington, Giants general manager Jerry Reese said.
The New York Daily News has reported that Pierce tried to hide Burress' gun.
Pierce declined to provide specifics about the incident Monday during a radio interview, but said that many facts of the case have been "misconstrued" and "distorted." He has hired an attorney but that he doesn't see himself being arrested, he said.
"Today has been a headache and that's about all I can say," he told WFAN.
The case drew the wrath of New York mayor Michael Bloomberg, who has waged a long fight against illegal guns during his time in office. He called for a full prosecution of state law that requires mandatory prison for carrying a loaded handgun.
"I don't think anybody should be exempt from that, and I think it would be an outrage if we didn't prosecute to the fullest extent of the law, particularly people who live in the public domain, make their living because of their visibility -- they're the role models for our kids," Bloomberg said.
He also lashed out at the hospital, based on the allegation that officials may not have properly reported the shooting.
"It's just an outrage that the hospital didn't do what they were legally required to do. It's a misdemeanor, it's a chargeable offense, and I think the district attorney should certainly go after the management of this hospital. The lame excuse that they didn't know -- this is a world-class hospital," he said.
The hospital said in a statement that officials "take this very seriously, and are conducting a thorough investigation into why this gunshot wound was not reported to the police department in a timely fashion."
Myrna A. Manners, the hospital's vice president for public affairs, told The New York Times: "It's clear that not reporting a gunshot wound is a violation of our policies and procedures." Late Monday night, she told the paper that a person responsible for not reporting the gunshot wound had been suspended.
Brafman refused to respond to media reports about an alleged coverup, other than to say: "I think a lot of what's been in the press is not accurate."
"If they let him play, he will be able to play," Brafman said. "I think he will be a superstar for the rest of his career."
"My hope is that it plays out well and he can continue his career, because he's a good person I think, with a brilliant athletic career. And it would be a terrible sadness if an isolated incident could ruin a life," Brafman said.
Police expressed frustration with the NFL and Giants officials, saying they were promised that Pierce would appear at a police precinct Monday where Burress went before heading to court. But Pierce didn't show. Detectives also went to Pierce's house in New Jersey and he was not there.
Police said the Giants did send a member of their medical staff to the precinct who may be able to shed some light on what transpired the night of the shooting, and presumably to relay Pierce's version of events.
"It was a universe of silence after this shooting," said Paul Browne, NYPD Deputy Commissioner for public information.
The Giants released a statement disputing the police version of their involvement. "We are working closely with the police and NFL Security," it said. "In the early hours of Saturday morning, as we started to get a sense of what we were dealing with, we did, in fact, notify NFL Security, which then contacted the police."
The NFL is monitoring the case.
"This is a law enforcement matter and we are continuing to cooperate fully with the police," league spokesman Greg Aiello said in a statement. "In addition, it will be reviewed under our league policies."
Brafman met with Burress for about an hour Sunday at the player's home in New Jersey.
"I would ask that his fans, the Giants and the media withhold judgment in this matter until all of the facts have been disclosed," Brafman said in an earlier e-mail to the AP.
Brafman is a well-known criminal lawyer who has defended mobsters and other high-profile figures, including hip-hop impresario Sean "Diddy" Combs on a bribery and gun possession charge in 2001.
Giants running back Brandon Jacobs said he spoke to Burress on the phone after Sunday's game.
"I called him and made a few jokes about the situation and his laugh is what I wanted to hear," Jacobs said, according to Newsday. "If he didn't laugh I knew he was going to be down, which he shouldn't be down. It's a mistake that happened, something that shouldn't have happened and that's that."
Before the shooting, Burress already had been ruled out of the game because of a leg injury.
The Giants say that Burress is required to report to the team's facilities on Tuesday because he's an injured player and injured players require treatment.
Giants spokesman Pat Hanlon told ESPN's Sal Paolantonio: "We have tried to reach out to him and we have not heard from him"
Giants coach Tom Coughlin said he spoke to his players about Burress' situation but wouldn't get into specifics.
"We all are upset about what happened with Plaxico, and hopefully he's going to be fine and so on and so forth. That's our first concern," Coughlin said. "Once that was taken care of, we knew that he was OK, then the guys got right back to focusing on the reason we were here."
Coughlin wouldn't address Burress' future with the Giants, saying only, "Questions of that nature will be discussed going forward, I'm sure."
The team is considering placing Burress on the non-football injury reserved list, which would make him ineligible for the remainder of the season, sources told ESPN's Chris Mortensen. It also would allow the Giants to recover some money already paid to Burress.
According to a person who has seen the contract, Burress' deal signed Sept. 8 includes $4.25 million in signing bonus, of which he has already received $3.25 million. The remaining $1 million is due to be paid within 15 days of Dec. 10, or by Christmas.
The Giants, according to a team source, are currently consulting with team legal counsel to determine if they are within their rights to withhold that remaining bonus money. Additionally, if Burress is suspended for conduct detrimental to the team or incarcerated, they may be able recoup the entire $4.25 million.
Burress caught the go-ahead touchdown pass in the Giants' Super Bowl victory against the New England Patriots in February, following a regular season in which he scored a career-high 12 TDs. He was rewarded with a $35 million, five-year contract, only hours before the current season.
Burress has 35 catches for 454 yards and four touchdowns while constantly drawing double coverage this season.
"I don't think people understand how good of a person he really is," fellow receiver Amani Toomer said after catching a 40-yard touchdown pass in the Giants' victory Sunday. "A good heart. I think he's a good guy."
Information from ESPN's Chris Mortensen, Rachel Nichols and The Associated Press was used in this report.