Toronto used six relievers for 7 1-3 innings in Friday night's 11-5 loss to the White Sox. Chad Jenkins pitched 2 2-3 innings in the series opener in Chicago and was optioned to Buffalo after the game.
The 26-year-old Drabek began the season in Buffalo's rotation, but moved to the bullpen in mid-June. He had a 3-1 record with a 2.77 ERA in 16 relief appearances with the Bisons.
Drabek is 8-15 with a 5.37 ERA in 37 games, 30 starts, in parts of four seasons with Toronto.
The Blue Jays announced Drabek's promotion before Saturday night's game against the White Sox.