Mayza was attempting to grab a bunted ball during a safety squeeze play and collided with Twins base runner Nick Gordon.
After lying on the ground in pain, Mayza continued to clutch his right shoulder as he was helped up and assisted off of the field.
The 30-year-old Mayza, who took over for starter Mitch White in the fifth, gave up two runs, both earned, on three hits over two-thirds of an inning.
Right-handed pitcher Anthony Bass came in to replace Mayza with the Blue Jays trailing 5-2.
Minnesota went on to win 7-3.