Laval police spokesman Franco Di Genova said the man may be suffering from a mental illness.
Di Genova said police were responding to a phone call about an altercation at a triplex on Rose de Lima Avenue.
An officer discovered an 85-year-old man and a 40-year-old man in the building, both suffering from stab wounds.
The two men were taken to hospital.
Police said they found an empty rifle case in the suspect's nearby apartment.
Soon after the discovery, police said they found the suspect a few streets away.
Di Genova said the suspect was shot in the upper body after he pointed a rifle towards officers.
The man is being treated in hospital.