Happ, who won 20 games for the first time last year, left Sunday's start against Baltimore in the fifth inning with a sore elbow. On Monday, he had an MRI, which revealed no structural damage.
Manager John Gibbons says he's optimistic Happ will be ready to return at the end of his DL stint, or shortly after. Happ is 0-3 with a 4.50 ERA.
Right-hander Aaron Sanchez, who is on the 10-day DL because of blister on his middle finger, underwent a procedure Monday to remove a portion of his nail. He will try playing catch in the next few days.
Also Tuesday, the Blue Jays recalled right-hander Danny Barnes from Triple A. He takes the roster spot of left-hander Matt Dermody, who was optioned to Buffalo on Monday.