The Blue Jays placed Burr on the 60-day injured list Friday due to a strained right rotator cuff.
Burr exited a relief appearance Wednesday with a shoulder injury, and further testing revealed he strained his right rotator cuff. The injury will sideline him for at least two months, and he won't be eligible for activation until Sept. 10. He missed the first three months of the season with issues in the same shoulder. The Blue Jays selected Tommy Nance's contract from Triple-A Buffalo in a corresponding move.