Morrow was hurt in the final inning of his outing Friday against the Pirates. He finished the inning and told the training staff of the injury when he returned to the dugout.
"He said he just felt something pop," Gibbons said.
Toronto recalled reliever Chad Jenkins from Triple-A Buffalo. In his only prior appearance for the Blue Jays this season, he allowed three runs and five hits in 1 2/3 innings April 26 against Boston.
Morrow, 1-2 with a 5.93 ERA this season, flew to Arizona on Saturday to meet his personal doctor for an MRI.