Rogers, who had been at the team's suburban training facility in recent days taking part in a voluntary offseason program, was stopped at a security checkpoint on Concourse C when officials spotted a loaded .45-caliber handgun in his bag, police said in a statement.
He was arrested at 12:15 p.m. ET "without incident," transferred to a downtown processing center and booked for carrying a concealed weapon, a third-degree felony.
Sgt. Sammy Morris of the Cleveland Police Department said Rogers was held in the city's jail overnight Thursday and remained there Friday morning.
No charges have been filed yet, police said, though the 31-year-old Rogers could face federal fines for carrying the firearm.
It's not yet clear what Rogers, who lives in Houston during the offseason, told officials about the gun or whether he has a permit for it. It's also unclear whether he was traveling with anyone.
Browns president Mike Holmgren issued a statement saying the team was aware of Rogers' arrest.
"We will continue to gather additional information, and until the legal process has taken its course, we will reserve any further comment," the statement said.
A message seeking comment was left with Rogers' agent, Kennard McGuire.
Beyond his legal problems, Rogers, arguably one of the Browns' best players, likely will face league penalties if it is determined he violated the NFL's player-conduct policy.
A three-time Pro Bowler who has played two seasons with the Browns, Rogers missed Cleveland's final five games last season after breaking his leg Nov. 29 against Cincinnati. He was acquired by the Browns in 2008 in a trade with Detroit for cornerback Leigh Bodden and a third-round draft pick.
Rogers came to the Browns with a spotty reputation. He was suspended for four games in 2006 for taking a banned substance to control his weight. In 2007, an exotic dancer claimed he inappropriately touched her at a club in Detroit, but an investigation cleared him.
The Lions also had issues with Rogers' weight and his commitment.
Rogers made the Pro Bowl in his first season with Cleveland, recording 4½ sacks and 81 tackles in 16 games. Blessed with amazing quickness for a man his size (6-foot-4, 350 pounds), Rogers has also excelled in blocking field goals and extra points. Before getting hurt last season, Rogers blocked one field goal -- the 13th of his career -- and two extra points.
Rogers and Browns coach Eric Mangini got off to a rough start before last season. Rogers had felt slighted when Mangini, weeks after being hired by Cleveland, did not acknowledge him at an awards banquet at a downtown hotel. Rogers reportedly asked to be traded, but the two met and patched up any differences and Mangini often praised Rogers, known to his teammates as "Big Baby," for his leadership last season.
Rogers' arrest is just the latest incident involving high-profile athletes and guns.
Washington Wizards guard Gilbert Arenas was recently sentenced to 30 days in a halfway house for bringing guns into his team's locker room; New York Giants wide receiver Plaxico Burress is serving two years after pleading guilty to a weapons charge; and Cleveland Cavaliers guard Delonte West is facing weapons possession charges after he was arrested in Maryland.