The fire began around midnight in the three-storey building on Dagenais Street.
It took 80 firefighters to bring the fire under control.
By then, the triplex was destroyed. Two neighbouring buildings were damaged, but residents were eventually able to return home.
Fifteen people were forced out of their homes. Three suffered smoke inhalation, including a 25-year-old woman who was taken to hospital.
Police say firefighters found suspicious elements on the scene and transferred the case to Montreal police.