The Tigers placed Flaherty on the 15-day injured list Tuesday with a right flexor strain.
Flaherty's injury may have played a part in his performance during his start Monday, in which he gave up three earned runs in just four innings against the Cubs. He'll now be forced to miss a few turns through the rotation while he recovers, and the Tigers will bring Ty Madden up from Triple-A to add some extra depth to their bullpen.