The service says 20-year-old Rhett Mutch was shot in an encounter with Victoria police officers shortly after 11 on Saturday morning.
Mutch was taken from the scene by an ambulance, but died before he made it to hospital.
Both the coroners' service and the Independent Investigations Office are investigating the death.
In the hours after the death, Victoria Police Chief Frank Elsner said officers were responding to a 911 call from a home in the city's James Bay neighbourhood.
Elsner says officers were confronted by the man when they arrived at the home.