A man has been arrested over the murder of an Israeli student, 21, who was killed close to her university in Melbourne.

Aiia Maasarwe’s body was found by passers-by early on Wednesday near La Trobe University's Bundoora campus in the northeast of the Australian city.

She was attacked while speaking on the phone to her sister, police said.

A man, 20, was arrested over her murder in a nearby suburb on Friday. Victoria Police did not immediately provide further details.

Police, who believe Ms Maasarwe was followed off public transport before she was killed, described her as an Israeli national.

"This is a horrendous crime that has been inflicted on an innocent member of our community," Detective Inspector Andrew Stamper told a news briefing on Thursday.

"Our presumption is that this was a random attack and opportunistic," he said.

It was the second time in seven months that a young woman has been killed on her way home at night in Melbourne, which has an active night life and is popular with overseas university students.

Police said Ms Maasarwe had taken a tram home after seeing a comedy show. She had been speaking with her sister on the phone at the time of the attack and her sister alerted authorities, Mr Stamper said.

"She heard the sound of the fall, the phone falling to the ground and heard some voices and that was it," he added.

Ms Maasarwe's family members arrived from Israel on Thursday.

The 21-year-old had been in Melbourne on a six-month study abroad programme as part of a degree at Shanghai University.