R.A. Dickey is slated to throw against the Rays on Saturday, following Friday starter J.A. Happ.
Toronto manager John Gibbons says the move was made to give Stroman more rest even though the team had an off day Thursday.
"We've been trying to do that all year," he said before Friday's game. "And Buehrle's been good against Tampa too. It makes sense."
The 23-year-old Stroman, a pleasant surprise for the Jays this season with a 10-5 record, has pitched 114 2/3 innings in the majors as well as 35 2/3 innings at triple-A Buffalo.
He is 1-1 in two starts against Tampa this season with a 5.73 earned-run average and has yet to face Baltimore.
Buehrle is 2-0 with a 2.08 ERA in five starts against the Rays this season. He has not had the same success against the Orioles, going 1-2 with a 4.67 ERA in three starts.