Louis Bourgeois was found severely beaten around lunchtime Monday behind the building on Gouin Boulevard, according to the director of the Villa Saint Martin, Gabriel Côté.
Côté said the priest was headed to clean his camper van parked behind the building when he was attacked.
Officials at the Jesuit residence think Bourgeois might have surprised a squatter living in a trailer on the property.
Bourgeois suffered severe injuries to his head and face and might lose an eye as a result of the attack. Côté said the priest's wallet and personal belongings were with him when he was found.
Police still have no suspect.