The first took place around 11:20 p.m. Sunday in a partially-used building on Laprairie Street near St. Patrick Street in the Southwest borough.
Firefighters found materials at the site that led them to suspect that the fire was deliberately set.
Montreal police arson unit officers were called to the scene.
Their investigation continues.
Arson investigators are also collecting evidence in two incidents in Rivière-des-Prairies that saw two cars burned overnight.
The first incident took place around 12:20 a.m. and saw a car set alight in the driveway of a residence at Pierre Baillargeon Avenue and Albert Chamberlain Street.
Police say flammable materials had been thrown into the car and the arson unit was called in.
Later, at around 2:15 a.m., police received reports of a second car on fire in the driveway of a residence on 28th Avenue at René Descartes Avenue.
Calls to 911 reported a small explosion followed by a fire in the car.
Arson unit detectives were called to the scene.
Police patrols in Rivière-des-Prairies were intensified as a result of the incidents.