Bowers was arraigned Monday on charges of criminal possession of a weapon and posted $10,000 bond. Team officials said Tuesday they won't comment until they have all the facts.
According to authorities, Bowers was arrested at LaGuardia Airport as he was about to board a U.S. Airways flight to Raleigh, N.C. The .40-caliber weapon was found during a search of his carry-on bag.
Efforts to reach his attorney were unsuccessful.
Bowers played college football for Clemson and was selected by the Buccaneers in the 2011 NFL draft.
Former New York Giants receiver Plaxico Burress was arrested on the same charge after he accidentally shot himself in a nightclub in 2008. He eventually served time in prison.
Information from The Associated Press was used in this report.