The Rays placed Cleavinger on the 15-day injured list Saturday due to left forearm tightness, Marc Topkin of the Tampa Bay Times reports.
The 32-year-old southpaw may have picked up the injury during Friday's outing against the Rangers, when he allowed two runs on two hits (including a home run) and a walk while failing to record an out. He's eligible to return from the IL on Sept. 20, and he expressed confidence Saturday that he would pitch again this season, per Ryan Bass of Rays.tv. Right-hander Ty Johnson had his contract selected from Triple-A Durham in a corresponding move.