Tate was injured rolling out to his left to open Calgary's second possession of the game. He put his left arm down to brace himself while being hit by Toronto's Derrick Summers.
Tate remained down for some time before walking off the field, then to the Calgary dressing room. He was replaced by veteran Kevin Glenn.
Tate, who is right handed, joined his teammates on the sidelines in the second quarter with his left shoulder heavily wrapped and his arm in a sling.
The Stampeders starter guided Calgary to a 69-yard, seven play drive to open the contest that he capped with a four-yard TD strike to Rob Cote at 3:36 of the first quarter.