Police appealed to the public for help tracking down the killer.
Here's what we know so far about what happened.
According to her social media pages, the talented student had been studying Chinese and English at Shanghai University, and then spent several months in Melbourne on an overseas program at La Trobe University.
Ms Maasarwe was reportedly planning to go to China to work with her father's business after her studies.
Ms Maasarwe was described as "happy", "adventurous" and "smart".
The death has sent shockwaves through Melbourne, which was ranked among the five safest cities in the world on The Economists' 2017 Safe Cities index.
Israel's diplomats in Canberra and the Foreign Ministry's Department for Israelis Abroad are working to bring the woman's body home to Israel for burial.
Event organiser Arun Chandran said Ms Maasarwe had joined a few of the group's tours in the past, including one to see kangaroos in the wild in December a year ago.
"She's positive, she likes to have fun, she's a very friendly person you know. It was quite refreshing to talk to her", he said.
"I found out yesterday evening", her classmate said.
Ms Maasarwe's bag was split open and some of its contents were removed, Mr Stamper said.
"It's just a sense of disbelief", he said.
"Aiia Maasarwe was like so many other women and girls - she was out meeting friends, exploring the city, taking in shows - she should've been able to do that safely".
After that event, she attended a comedy show at The Comics Lounge in North Melbourne.
Victoria police have released CCTV footage and objects of interest in the death of Israeli student Aya Masarwe.
Anyone who may have seen suspicious behaviour on that tram, which has a stop some 100 metres away from where the woman's body was found, has been urged to contact police.
A brutal, opportunist killer is on the loose in Melbourne, with Australian police desperately appealing to the community for information as they investigate the murder of 21-year-old Israeli student Aiia Maasarwe.
Stamper said police believed it was a random and opportunistic attack, but he would not say whether she had been sexually assaulted.
Disturbingly, Ms Masarwe's uncle, Rame Masarwe, said Aia was speaking to her sister using FaceTime until "her phone fell" on the night she was killed. "We think America is risky, not Australia".
She was on the phone, Facetiming her sister about 12.10am, when her sister noticed the phone drop and voices muffled in the background.
"The day before, my wife had said to me, 'We'll have to go to Australia, Australia's very safe, very nice, '" the victim's uncle Rame Maasarwe told national broadcaster ABC from the United States.
"All I will say is, this was a horrific attack".
"This was an horrendous, horrific attack inflicted on a completely innocent young woman who was a visitor to our city", Detective Inspector Andrew Stamper told reporters in Melbourne.
Main Drive has been cordoned off by police.
About 7:00am on Wednesday, the body of Ms Maasarwe was discovered by passers-by outside the nearby Polaris shopping centre.
Investigators retrieved a black baseball cap engraved with the number "1986" and a two-tone gray T-shirt that they believe were worn by the assailant at the crime scene, which they described as "very distressing".