Tate was diagnosed with a strained forearm muscle in his throwing arm on the weekend. He did not finish last Friday's 36-21 loss to the Saskatchewan Roughriders, leaving with about five minutes remaining in the game.
The Alouettes host Calgary on Friday.
Tate was on the field for practices Monday and Tuesday, but backup Kevin Glenn took snaps both days. Tate continued to practise footwork and simulate a throwing action without the football Tuesday.
"It's still sore," Stampeder coach and general manager John Hufnagel said of his quarterback's arm. "Nothing has improved to a point where he can throw yet.
"If he's throwing the ball tomorrow effectively, then he'll play."
Calgary and Montreal both opened the season 1-1.
Tate said he felt less pain in his arm than he had the previous day.
"Still day-to-day, I guess," the 27-year-old said. "That's all I can do. Wake up every morning, hope it feels better, get some treatment and come out here and have a good practice."