The fire is on Girouard Avenue near Sherbrooke Street, and started at around 2:45 a.m.
The building, which has four units on two floors, had to be evacuated.
No one was hurt and the 20 residents are being cared for by the Red Cross and Sun Youth.
Fire officials believe the fire started on a balcony behind the building, but say it's too early to know the cause.
They say the fire is not yet under control and they are concerned it may spread to a neighbouring building.
About 100 firefighters are on the scene.