Eight apartments in the building on the corner of Queen Mary Road and Cedar Crescent were heavily damaged.
No one was injured, according to firefighters.
The fire started on the first floor of the four-storey building. It spread through the ventilation system, making it hard to extinguish.
According to firefighters, 68 people were evacuated from the building. The Red Cross deployed a team of volunteers to the scene this morning.
"We will offer victims shelter and clothing for the next few days,” said Carl Boisvert, spokesman for the Red Cross.