McKenzie was optioned to Triple-A Columbus on Thursday.
McKenzie returned to the major-league mound as the starter in Wednesday's game and allowed one hit and three walks while striking out five in five scoreless innings. Although he pitched effectively in the no-decision, he'll return to the minors after outfielder Bradley Zimmer was recalled in a corresponding move. However, McKenzie could return to the big-league club when his next turn in the rotation comes up Monday. Cleveland has a doubleheader against the White Sox that day, and McKenzie would be eligible to return earlier than normal if he's designated as the club's 27th man for the twin bill.