The team said Morrow suffered a left oblique strain. He's listed as day-to-day.
Morrow felt something was not right after he threw ball two on a 1-1 pitch to Bryce Harper. Morrow had allowed a leadoff double to Steve Lombardozzi.
The right-hander walked from the mound and went down the stairs to the clubhouse on his own after being checked by the training staff and manager John Farrell on the field.
Chad Beck took over from Morrow.
On May 30, he was removed from a start against the Baltimore Orioles with a bruised right shin after was hit by a batted ball.
He pitched a two-hit shutout in his next start, helping Toronto defeat the Chicago White Sox 4-0 on June 6.