The shooters were not among the victims, and police said they fled the scene after they opened fire.
"Apparently the offenders left in a vehicle," a police source told AFP.
It is not clear how many shooters there were or why gunfire erupted at the party.
Police received several calls at 5:05 am (1205 GMT) reporting gunfire at the private party, where some 50 people were gathered.
Emergency workers took five people to the hospital, including two with life-threatening injuries.
Photos on social media showed the streets around the house where the shooting occurred sealed off with police tape.
Calgary in western Canada is home to about one million people.
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