Moran was optioned to Triple-A St. Paul on Saturday, Do-Hyoung Park of MLB.com reports.
Moran rejoined the Twins' bullpen Monday but made just one relief appearance during his stint with the big-league club. He allowed a run on three hits and no walks while striking out five in three innings Wednesday against the Red Sox but will head back to the minors after Tyler Mahle (shoulder) was reinstated from the injured list Saturday.