The club purchased the contract of right-handed pitcher Ramon Ortiz from Triple-A Buffalo on Saturday.
Morrow is 2-3 with a 5.63 ERA in 10 starts for Toronto this season. He left his last start after two innings with soreness in the arm.
The 40-year-old Ortiz will make the start on Sunday in San Diego in Morrow's place. Ortiz, 1-2 with a 5.01 ERA, has appeared in six games -- three starts -- for the Blue Jays this season.
Toronto also recalled righty Mickey Storey from Buffalo following Friday's 17-inning game against the Padres.