Part of the roof, about the size of a couple of school buses, tumbled down the side of an exterior wall onto some trees. Officials did not report any injuries.
Sylvain Cuillerier, a spokesman for Montreal's fire department, said a 20-metre by 30-metre section of the roof was blown off the top of the arena.
Several members of Canada's national short-track speedskating team, which trains at the arena, gathered outside the building to survey the damage. They wondered whether their training session on Friday morning would still be a go.
"Nothing's confirmed yet, I have no clue, but my guess is they might have to test the roof to make sure," said Liam McFarlane, a team member for the last six years and a former Olympic alternate.
"Maybe we'll be off a day. We're heading off to Calgary in a week so either way we'll have ice."
The sounds of twisting, vibrating metal still echoed through the area hours after firefighters said the incident occurred.
At one point, a piece of sheet metal, around the size of a small coffee table, bounced down the street at high speed like a tumbleweed.
The rink, adjacent to the Olympic Stadium, has served as the home of Canada’s national short-track speedskating team.
It opened in the early 1960s, was a venue for events at the 1976 Summer Olympics and has hosted junior hockey over the decades.
The arena has a capacity of 4,750 and is perhaps best known locally for the statue of Richard in front of the building.
Dozens of people in the residential area gathered at the scene behind the police tape. Police closed a nearby subway station and structural engineers were inside the building.
Scaffolding could be seen outside the building and McFarlane said construction crews had been doing work in recent days.
"It's slightly disconcerting, that's for sure," he said, staring at the mangled metal strewn on the arena lawn. "But it's the outside (of the building) and the winds are pretty strong, so it probably could have happened anywhere."