A wide piece of the roof of the Maurice Richard Arena, about 600 square metres in size, was blown off by heavy winds that sent pieces of debris flying around the previous night.
"Big winds simply took off part of the roof," Tremblay said Friday.
"We can be thankful that nature didn't cause a more tragic incident."
He said an investigation would help determine what caused parts of the structure to peel away.
A metro station next to the arena, which is just outside Montreal's Olympic Stadium, remained closed Friday morning.
The rink has served as the home of Canada's national short-track speedskating team. Some members of the national team rushed to the site yesterday to witness the damage.
The building 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.