Coke, 30, has been sidelined since April 25 because of a strained left groin. Coke has an ERA of 8.31 in nine appearances. He owns an ERA+ of 103 across parts of six major-league seasons.
In order to make room on the active roster, the Tigers have optioned right-hander Luke Putkonen back to Triple-A Toledo. That swap means Detroit will now have three lefties in the bullpen, as Coke joins Drew Smyly and Darin Downs.