Victoria Police were responding to reports of a man with a machete in South Melbourne about 5pm on Saturday when the incident happened.
Two officers had found a man and were arresting him in a street when a white SUV drove at them, police said.
The car hit the male senior constable, who fired four shots at the vehicle, hitting the 34-year-old female driver and 26-year-old male passenger.
The woman died at the scene, the passenger was taken to hospital with non-life threatening injuries, and the officer was taken to hospital with serious but non-life threatening injuries.
The other police officer was unharmed, and the man with the machete was taken to hospital for observation.
Acting Assistant Commissioner Therese Fitzgerald said police were trained to respond to such incidents, adding the officer was "extremely lucky" not to suffer worse injuries.
"This is the kind of incident that all of or members are at risk of at any time," she told reporters.
"The police members are trained to respond in a certain way and that's what's taken place."
Homicide detectives are investigating the incident, and will be overseen by the Victoria Police Professional Standards Command.
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