Thames suffered the injury Wednesday night while making a potential game-saving catch on a fly ball by Minnesota's Joe Mauer in the bottom of the eighth inning. The catch kept Detroit ahead, 3-2, which turned out to be the final score.
"(The injury) pretty much stinks," Thames said on the Tigers' Web site after the game.
"Right now, we need an outfielder bad," said Manager Jim Leyland after Thursday's 4-3 victory.
Thames, who hit his third career grand slam home run July 7 against Boston, is batting .252 this season with 11 homers and 32 RBI in 155 at-bats.
To take his place on the roster, Detroit bought the contract of outfielder Timo Perez from Triple-A Toledo.
Perez was batting .322 with 48 RBI.