The Twins optioned Moran to Triple-A St. Paul on Wednesday.
The transaction clears room on the 26-man active roster for right-hander Sonny Gray (pectoral), who was activated from the 15-day injured list in advance of his scheduled start Wednesday in Seattle. During his two-and-a-half-week-long stay with the big club, Moran made five appearances in relief and collected one save while striking out 10 in 7.2 innings and giving up two earned runs on five hits and seven walks.