The Tigers placed Finnegan on the 15-day injured list Thursday, retroactive to Wednesday, with left groin inflammation.
Finnegan had struggled in his last two outings Sunday and Monday. Both games were in Toronto, where he gave up four earned runs on six hits with one strikeout across 1.1 innings through the two games. The Tigers still have a slim chance at making the playoffs as of Thursday, but Finnegan's season is likely over. In a corresponding move, the Tigers recalled Ty Madden from Triple-A Toledo.