The body of Aiia Maasarwe, 21, was found near La Trobe University in the city's north. She had taken a tram home late on Wednesday after a comedy show.
Her sister "heard the sound of the phone falling to the ground and heard some voices", officer Andrew Stamper said.
Police are searching for the killer.
They have not ruled out the possibility that Ms Maasarwe was sexually assaulted, Melbourne's Age newspaper says, with known sex offenders "an active line of inquiry".
"Our presumption at this stage is that this was a random attack and opportunistic," Detective Inspector Stamper told reporters.
Ms Maasarwe's sister, worried about Aiia, is reported to have called Australian police around the same time the body was found on Thursday morning outside a shopping centre.
A black cap emblazoned with "1986" and a grey t-shirt were found near the crime scene, and are being forensically tested. Police are also scouring CCTV footage for clues.
"Someone in the community knows about this. Someone has gone home on Tuesday night, or in the early hours of Wednesday morning, maybe with blood on them, missing items of clothing. Somebody knows about this," said Mr Stamper.
Aiia Maasarwe's father has arrived to identify the body, which the Israeli embassy said it would assist with returning to Israel.
Last June the killing of 22-year-old comedian Eurydice Dixon sparked fresh anger and debate about violence against women in Australia.
Ms Dixon was raped and killed while walking home after a performance in Melbourne.
That followed a similar case in 2012, when Irish woman Jill Meagher was raped and murdered in Melbourne's inner north while walking home - prompting mass rallies to remember her and raise the issue of women's safety.