The injury occurred while Morales was running out a single in the second inning of Monday night's game against the Orioles. Morales remained on first base after being examined, but he was replaced by a pinch runner after advancing to second on a fielder's choice.
Toronto manager John Gibbons expects Morales to return after the minimum stay on the DL, adding that Morales will likely start taking batting practice on Wednesday or Thursday.
Morales is batting .227 with 1 home run and 6 RBIs in eight games.
The Blue Jays filled the roster spot by recalling reliever Tim Mayza from Triple-A Buffalo on Tuesday. The left-hander was 1-0 with a 6.88 ERA over 17 innings for Toronto in 2017.