The fire started just before 1:30 p.m. in the building near the corner of Paxton and Guy streets.
More than 30 fire trucks and 80 firefighters responded. Many of them helped get residents out of the 84-unit building.
At least one person was transported away from the building on a stretcher, but Urgences-santé said no major injuries had been reported.
The cause of the fire is still under investigation.