Madden allowed three runs on four hits and a walk across three innings of relief during Saturday's 4-0 loss to the White Sox. He struck out two.
Madden (1-0) allowed a run on five hits and a walk while striking out seven over five innings to earn the win over the Athletics on Sunday.
Madden is no longer listed as the starter for Sunday's game versus the Red Sox but could be used as a bulk reliever that day, Jason Beck of MLB.com reports.
Madden is scheduled to start Sunday's game against the Red Sox at Comerica Park.
The Tigers selected Madden's contract from Triple-A Toledo, and he will start in Monday's series finale against the White Sox.
Tigers manager A.J. Hinch said that Madden will be called up from Triple-A Toledo to start Monday's game against the White Sox in Chicago, Evan Petzold of the Detroit Free Press reports.
Madden was promoted to Triple-A Toledo on Monday, Emily Waldon of Baseball America reports.
Madden has a 2.43 ERA, 1.03 WHIP and 50 strikeouts in 37 innings over his last seven starts for Double-A Erie.