The 18-year-old woman was returning from a night out with friends when she was allegedly confronted by a man and stabbed about 1am outside a house on Miller Grove in Kew, according to police.
The woman was taken to hospital with what was initially believed to be life-threatening injuries.
She is now in a stable condition and recovering in hospital.
Soon after the attack, police began searching for an 18-year-old Camberwell man.
The death of the man is not being treated as suspicious and a report will be prepared for the coroner.