McCown was injured in Thursday night's 56-14 loss in Atlanta when he hit his throwing hand on a defender's helmet after releasing a second-quarter pass. McCown, who was unable to grip the ball, was replaced by second-year man Mike Glennon.
Glennon is expected to start in McCown's absence.
McCown, 35, signed a two-year deal with the Bucs this offseason. The 13-year-veteran has 420 passing yards with four touchdowns (two passing, two rushing) and four interceptions in three games this season.
The 24-year-old Glennon threw for 2,608 yards, 19 touchdowns and nine interceptions as a rookie last season, starting 13 games.
Tampa Bay (0-3) visits the Steelers (1-1) next Sunday.
- Chris Mascaro