More than 4,300 people have crossed into Canada seeking refugee status since January.
The majority of those have crossed into the province of Quebec, straining resources of government and community groups.
The stadium received the request for space last Friday.
Asylum seekers began to be moved into the building, one of Montreal’s most well-known landmarks, on Wednesday morning.
Canada has seen a significant increase in the number of people crossing illegally into the country between official points of entry and seeking asylum.
Over 3,300 people crossed into Quebec between 1 January and 30 June.