Franco will have surgery on Tuesday to repair a fractured hamate bone in his right hand and will be out for up to eight weeks.
In the bottom of the first, Franco left the game with a wrist and hand injury after he struck out against a 100.2 mph pitcher. Franco was examined by a doctor.
Taylor Walls is expected to get most of the playing time in place of Franco, who is hitting.260 with five homers, 23 runs and a.702 OPS in 58 games this season.
Franco was put on the injured list.
One of the three wild-card spots in the American League is currently occupied by the Rays who have lost three in a row.
The AP contributed.