On July 8, Quebec announced that they would introduce a vaccine passport by the fall — but would only use it to control access to locations like gyms, bars and restaurants if there is an outbreak.
https://globalnews.ca/news/8025474/canada-private-business-vaccine-passport/
There was an article about a vaccination passport being implemented in Quebec, but it didn't include an exhaustive list of the businesses that will require a vaccination passport.