Detroit made the move shortly before Wednesday's series finale. Verlander was scratched from his start late Tuesday night. Manager Brad Ausmus said the right-hander's back tightened during his previous start and the team is hopeful the former Cy Young winner will miss just one start.
Verlander began this season on the disabled list with a triceps injury.
To make room for Farmer, the Tigers optioned left-hander Ian Krol to Triple-A Toledo.
Farmer is making his second start this year for Detroit. He pitched five innings and took the loss against the Los Angeles Angels on May 28. He's gone 8-4 with a 3.56 ERA for the Mud Hens.
Tigers slugger Miguel Cabrera is getting the day off. He's batting .619 with five homers and 16 RBIs against Cleveland in 2015.