Myers was injured on the final play of a 3-2 loss Friday to the Boston Red Sox when his hand slapped the ground as he landed following a collision with center fielder Desmond Jennings. The collision led to a game-ending triple by A.J. Pierzynski in the 10th inning.
Myers, who also sat out Saturday's game, is batting .227 with five homers and 25 RBIs this season.
Tampa Bay recalled Jerry Sands from Triple-A Durham to replace Myers.
The 26-year-old Sands was batting .268 with 12 doubles, nine homers and a team-high 36 RBIs for the Bulls.
Infielder Tim Beckham (right knee surgery) was transferred to the 60-day DL.