Firefighters were called to the former Daly-Morin Windows and Shades factory on Victoria St. near 19th Ave. at around midnight.
The fire appeared to have started in more than one location and spread abnormally quickly, said Montreal Fire Department spokesperson Dennis Guy.
The investigation has been handed over to the police arson squad.
No one was inside at the time of the fire but several nearby buildings had to be evacuated.
On Monday morning, certain parts of the structure had collapsed and firefighters continued to douse the building with water, hoping to reach sections that could still be burning inside.
The former factory, which is being converted into condominiums, is more than a century old, said Lachine Borough Mayor Claude Dauphin.
Dauphin said he hopes some of the structure is still salvageable, adding it would be sad for the people of Montreal to lose such a landmark.
"It's an historical building. Many people of Lachine spent their life working there at Daly-Morin," said Dauphin.
The website for the development project indicates EMD-Construction is the principle entrepreneur responsible for the development.
No one from the condominium development partnership was available for comment Monday morning.