"Homicide Squad detectives have arrested a man as part of the ongoing investigation into the death of Aiia Maasarwe", Victoria Police said in a statement.
Earlier hundreds gathered at Latrobe University in a vigil for Maasarwe, 21, whose body was found behind a bush outside the auto park to the Polaris shopping centre in Bundoora about 7am on Wednesday.
"There are a lot of things that need to change. and a lot of these changes can start with the government itself and the choices they choose to make", she said.
The cap is black in colour and has "1986" printed on the front. "It's apparent or it seems that the female has been assaulted", Inspector Andrew Stamper told reporters near the scene on Wednesday.
Local police released footage showing the student making her way home shortly before the attack.
The devastated father of Aiia Maasarwe has arrived in Australia and has this afternoon visited the site where his daughter was murdered.
"She's positive, she likes to have fun, she's a very friendly person you know".
"This is giving me good feeling, but also in another way I am sad because this is the last place where my daughter was here", Mr Maasarwe said. The tram will depart from Parliament Station and travel to Bundoora, where her body was found.
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According to police it appears Aia had been assaulted, however the exact circumstances surrounding her death are yet to be determined. "And I am heartbroken she wasn't." .
Flowers and handwritten tributes have been left by mourners at the scene of the tragic discovery.
"Everyone has the right to get home safety", another read. She had been out at a comedy show, 9News reports, and was taking a tram as she spoke on the phone with her sister.
Vice-chancellor John Dewar addressed the emotional crowds, announcing that security for students would be ramped up.
Jane Pickering, the organiser of the silent vigil, said: "I felt that fear and rage and despair and sadness, and I thought of all the other women and girls who went out to see their friends on the same night and caught the tram home on the same night and how all of us live with that fear and risk".
Detectives are keen to speak to anyone who travelled on the route 86 tram, particularly between 11pm on Tuesday and 1am on Wednesday.
Police believe the attack was random and opportunistic.