Moran was optioned to Triple-A St. Paul on Wednesday, Dan Hayes of The Athletic reports.
Moran has been effective out of the Twins' bullpen this year, posting a 1.93 ERA, 31:15 K:BB and 1.20 WHIP in 23.1 innings over 20 appearances. However, he'll head to the minors since Tyler Mahle is slated to join the active roster after being traded from Cincinnati to Minnesota.