McMahon (thumb) is not in the lineup for Thursday's contest in Baltimore.
Outman (concussion) will begin a rehab assignment at Triple-A Toledo on Thursday, Chris McCosky of The Detroit News reports.
Rice went 2-for-5 with a solo home run in a 5-3 win against Baltimore on Wednesday.
Blackburn notched a hold against the Orioles on Wednesday, allowing one hit and issuing one walk while striking out one batter over one scoreless inning.
Manager Aaron Boone said after Wednesday's win over Baltimore that McMahon is slated to undergo X-rays on his left thumb, Bryan Hoch of MLB.com reports.
Bednar struck out one in a clean ninth inning to earn the save Wednesday against the Orioles.
Warren took a no-decision against the Orioles on Wednesday, allowing two runs on three hits and two walks in four innings. He struck out five.
Clark went 2-for-4 with a double and a run scored in Wednesday's 4-3 loss to the Pirates.
Lee went 1-for-2 with two walks and two runs scored in Wednesday's 4-3 loss to the Pirates.
Jansen (3-5) blew the save and took the loss Wednesday, giving up two runs on two hits in two-thirds of an inning as the Tigers fell 4-3 to the Pirates. He struck out one.
