Smith was recalled from Triple-A Buffalo on Thursday, Shi Davidi of Sportsnet.ca reports.
Smith was summoned back to the big-league bullpen to take the place of Taylor Cole, who was placed on the disabled list with a fractured toe. The 28-year-old owns a 5.40 ERA and 1.60 WHIP through five major-league innings this season, so he isn't expected to see anything other than low-leverage innings with the Blue Jays.