It took about 50 firefighters a few hours to control the blaze after they were called to the building in the old part of the city.
There were no reports of injuries and there were no visitors at the time because the museum is closed on Mondays.
"The good news in this string of bad news is that, at first glance, I think the works of art are not damaged," said museum director Michel Cote.
He said there was a lot of water on the floor of the museum, but noted a number of art objects were protected under glass.
"The firefighters also protected a number of objects and they came to consult us to find out which ones were our priorities," Cote added.
He said he expects the museum to be closed for at least one day, adding that about half of the museum will reopen quickly.
An exhibit of native art is being featured at the museum.
"We worked closely with native groups on the exhibition," Cote said.
"It's about our shared history with the aboriginals and we'll redo it because it's important to maintain contact with the native community."
He said the fire may have been caused by a motor that malfunctioned and that it was too early to evaluate the costs of the damage.
Annie Marmen, a fire services spokeswoman, said the flames were contained to the roof structure where crews had been working.
"The first information we got from 911 was that the fire was coming from where work was being done," Marmen said. "The first witnesses told us that's where it came from."
The museum opened its doors in 1988.