Bauer was the overall No. 3 pick by Arizona in the 2011 draft. He was sent to the Indians in the offseason as part of a three-team trade.
Known for his quirky training regimen, Bauer had a rough outing for the Indians on Wednesday, allowing four runs on five hits in three innings against the Los Angeles Angels. He had been one of several candidates for a late-rotation spot with Cleveland.
The Indians also optioned left-hander Scott Barnes and right-hander Corey Kluber to Columbus.
In addition, Cleveland re-assigned left-hander Giovani Soto, a non-roster invitee, to its minor league camp.