Delabar was sent to the DL retroactive to Saturday with right shoulder inflammation.
Toronto, which made the move prior to their game in L.A. against the Angels, has yet to replace Delabar in the lineup.
Delabar is 5-2 with a 2.90 earned-runs average in 49.2 innings pitched this season.
The right-hander is second among relievers in the majors with 75 strikeouts, four back of Kenley Jansen of the Los Angeles Dodgers.
The Blue Jays' relievers are the busiest in baseball with 388.1 innings pitched. Minnesota and Milwaukee are tied for second at 380.2.