Inge was injured in Monday night's 8-6 loss to Texas when he was hit by a pitch from Scott Feldman in the third inning.
Inge stayed in the game after being examined by Detroit's training staff, but was replaced in the field by Don Kelly for the top of the fifth.
X-rays showed a non-displaced fracture of his fifth metacarpal.
Detroit also announced Tuesday it is recalling right-handed pitcher Casey Fien from Triple-A Toledo. Fien is 1-1 with a 2.33 ERA and four saves in 31 appearances with the Mud Hens.