The Tigers recalled Madden from Triple-A Toledo on Tuesday.
With Jack Flaherty landing on the injured list with right flexor inflammation, Madden will join the Tigers' bullpen to give the team another multi-inning relief option. The 26-year-old righty owns a 4.71 ERA in 42 innings at Toledo but has been far more successful in the majors, posting a 3.15 ERA and 1.05 WHIP alongside a 23:5 K:BB across 20 innings.