McCown is scheduled for an MRI on Friday to determine the extent of the damage to his thumb.
The quarterback left the Buccaneers' Thursday night game against the Falcons late in the second quarter with a right thumb injury. He did not return and was replaced by second-year quarterback Mike Glennon.
McCown left the game after completing just five of 12 passes for 58 yards. He also threw an interception that was returned for a touchdown.
The Bucs fell to the Falcons, 56-14.
- Sarah Barshop