Morrow (2-3) has a 5.63 earned-run average, with 42 strikeouts. The 28-year-old left a start against Atlanta on May 28 after only two innings due to right forearm tightness.
The 40-year-old Ortiz (1-2) has appeared in six games this season for Toronto, with a 5.01 ERA.
Starting pitcher Ricky Romero was outrighted to Toronto's triple-A affiliate in Buffalo, N.Y., to make space on the Blue Jays 40-man roster.
Reliever Chad Jenkins had been optioned to Buffalo on Friday, with Mickey Storey moving up the Toronto.
The 27-year-old Storey has made two appearances for Toronto in 2013, recording a 7.36 ERA over 3.2 innings.