According to reports, an ice-skating course was taking place inside but no one was injured when a part of the roof blew off from the structure at around 7:30 p.m. ET.
The building is located on the corner of Viau Street and Pierre-de-Courbetin Avenue.
Police have blocked off a part of Pierre-de-Courbetin to proceed with debris removal and prevent other parts of the roof from blowing into the street.
Engineers were on the scene Thursday night, waiting to be able to solidify or remove loose parts of the roof, but high winds are making work difficult for them.
Fire officials said the metal sheet covering the roof was partly blown off onto the street. The structure under it seems intact but engineers will have to assess the situation.
Maurice Richard Arena was the venue for boxing and wrestling when Montreal hosted the 1976 Summer Olympics. The arena is now used for training by elite athletes and for hockey, figure-skating and speed-skating events.