Romo, who had started 30 straight regular-season games since replacing Drew Bledsoe in 2006, broke his right pinkie on the first play of overtime in a 30-24 loss at Arizona on Sunday.
"We don't know how long he'll be out. It depends on how fast that heals," coach Wade Phillips said Monday.
"I'd say week to week, depending on quickly he heals. Different people heal differently."
The injury, which Phillips said won't require surgery, leaves the Cowboys (4-2) with 40-year-old Brad Johnson as the starter. Johnson, who won a Super Bowl with Tampa Bay, hasn't started a game since 2006 in Minnesota.
"It's unfortunate for Tony to have to go through something like this," Johnson said. "He'll recover quick, he has a great attitude about it.
"At this time, it's really just important for the offense especially to just kind of catch on to my snap count, and the way we manage the huddle."
The Cowboys had no plans Monday to sign a veteran quarterback or trade for one before Tuesday's trade deadline, a team source told ESPN's Michael Smith.
Romo missed on three straight passes to start the overtime, having passed for 321 yards and three touchdowns in regulation despite heavy pressure. He was sacked three times and knocked down 19 times.
"Obviously, he had trouble throwing the ball that last series in overtime," Phillips said.
Romo, whose hand was heavily wrapped after the game, fumbled three times Sunday, losing one, but -- for the first time in nine games -- didn't throw an interception.
The Cowboys quarterback was feeling "down" about the injury, a source close to Romo who had spoken with him Monday told ESPN's Ed Werder,
though he likely will miss only three games, with the Cowboys' bye week coming four weeks from this past Sunday.
Romo and agent Ken Kremer were in the process Monday of determining whether they will seek a second opinion from a specialist.
Romo wasn't in the locker room Monday when it was open to reporters.
When linebacker Greg Ellis was told about Romo's broken finger, he got a somewhat stunned looked on his face and exclaimed, "Wow!"
Linebacker Bradie James said the players will have to rally around each other.
"We've got to play relentless football now without our signal-caller, our leader, our captain on the offensive side," James said. "That's the thing about a season; you never know what can happen. You hope you are playing some real good ball when things go down, so here we are and now we've got to make some adjustments and move on."
Receiver Terrell Owens refused comment, getting agitated when he saw cameras recording him.
"Today is not Wednesday," he said, referring to the day he routinely talks to reporters.
Through Sunday's games, Romo ranked second in NFC passing with a 103.5 rating. He has thrown for 14 touchdowns and been intercepted five times. He had his team-record 14th career 300-yard passing game Sunday in his 32nd start. That broke a tie with Troy Aikman, whose 13 were accomplished in 165 starts.
Johnson quarterbacked the Buccaneers to the NFL championship in 2002. He has been Romo's backup since last season and threw only 11 passes in 2007.
"I'm excited about the opportunity, worked hard to get here," Johnson said.
Johnson, in his second year as Cowboys backup, has seen only brief mop-up duty in Dallas, going 7-for-11 for 79 yards. Before coming to Dallas, Johnson started just one of his 145 career games with Minnesota (1993-98, 2005-06), Washington (1999-2000) and Tampa Bay (2001-04).
Johnson has completed 2,627 of 4,248 career passes (61.8 percent) for 28,627 yards with 164 touchdowns and 117 interceptions. He passed for 2,750 yards in 2006 with nine TDs and 15 interceptions -- only the third time in his career with more interceptions than TDs.
"It's going to be Brad to go in there and prove that he's not just here for the ride, he's part of this thing," Ellis said. "Every opportunity I've seen Brad step in on other teams, he's able to hold it down and get it done."
Another former Viking, Brooks Bollinger, will be Johnson's backup.
The Cowboys continued to evaluate Jones' partially torn left hamstring suffered Sunday, but a source told Werder the team expected the rookie to miss two to four weeks.
McBriar, who was carted off the field after his kick was blocked by the Cardinals' Sean Morey on the game's final play Sunday, will be out six to eight weeks with a broken right foot, the Pro Bowler told ESPN.com's Matt Mosley.
The Cowboys' regular season ends in 11 weeks, on Dec. 28 at Philadelphia.
McBriar's injury -- one main fracture and two hairline fractures -- won't require surgery. He said it likely happened
when he made contact with Morey's knee.
Hurd will undergo surgery for a high ankle sprain and miss the rest of the season.
Hurd hadn't caught a pass this season after first injuring the ankle in the Cowboys' final preseason game. He had 314 yards on 19 receptions in 2007.
Information from The Associated Press was used in this report.