No one was injured in the blaze in the city's Rosemont district which broke out Monday shortly after 8 a.m.
Montreal police arson investigators have been called in to help determine the cause.
"After examining the scene, the Montreal fire department investigators transferred the investigation to the Montreal police arson squad," said Montreal police spokesman Daniel Lacoursiere.
"Our investigators will go and examine the scene either today or tomorrow."
Firefighters responded quickly to the blaze. Even though the flames had spread to the top floor of the three-storey brick structure, they were able to bring it under control in about an hour.
But more than 35 people were forced to scramble outside until the fire was extinguished. Luckily, frigid temperatures that had gripped the city in recent days had given way to milder weather.
Red Cross spokeswoman Genevieve Dery said all the residents except those in six heavily damaged apartments were expected to get back into their homes on Monday.
"From these six apartments, there's only three people who have asked for our help," said Dery, explaining that those people would be put up in hotels for the next three days.
She could not say how many other residents there were in the six apartments but said they had opted to stay with family.
The Red Cross and the city's Sun Youth social service agency also helped the fire victims with other needs, such as clothing.
Dery noted the cruel timing of the blaze.
"It's always a terrible event (when there's a fire) but at this time of the year, for sure it's sad."