Cleavinger was optioned to Triple-A Oklahoma City on Sunday, Eric Stephen of SBNation.com reports.
The 28-year-old was promoted Friday when Clayton Kershaw (pelvis) was placed on the injured list and will return to the minors after firing a scoreless inning Saturday. Cleavinger has given up one run with a 4:2 K:BB over 2.2 frames in the majors this season.