Officers responded to the 1600 block of Murdoch Road, near Pickering Avenue, just before 9 p.m. on Monday.
Investigators say two men, who live in separate apartments in the same building, were in the vestibule when an argument turned physical.
They say a man in his 70s opened fire, shooting 42-year-old man was shot in the face.
He was taken to the hospital in critical condition.
Detectives are interviewing the alleged shooter.