The body of Aiia Maasarwe, 21, was found in scrub not far from where she got off a tram at the northern suburb of Bundoora late on Tuesday night.
Police say the Palestinian Arab of Israeli citizenship suffered a “horrific” assault and have launched a widespread hunt for her killer.
Morrison says Maasarwe’s murder is “just so shocking”.
“I mean, I’m speechless,” he told reporters in Fiji on Friday.
The prime minister said his heart went out to Maasarwe’s family, though he could not begin to think of what he would say to them.
“I know what I’m thinking about her attacker. I expect it’s the same thing that all other Australians are thinking today,” he said.
“I know the police will do their job and they’ll deal with it. But the rest of Australia has to wake up today and deal with the most despicable of crimes.
“My heartfelt condolences on behalf of Jenny and myself and my family, to her family, and I just I pray you can find whatever comfort you can in the worst of all circumstances.”
The prime minister stressed every woman and person in Australia should be able to travel home safely and that the government must remain “forever vigilant” to the issue of male violence against women.
Shorten said the murder doesn’t reflect the Australia or Melbourne he grew up in.
He said his feelings for the grief of Maasarwe’s family were strong but he wanted to reassure them Australia’s police are among the best in the world.
“They will successfully catch, and our legal system will punish, the wrongdoer,” he told reporters in Brisbane today.
The Labor leader also criticised Victorian senator Derryn Hinch for revealing graphic unconfirmed details of the crime on social media.
“People who are in positions of power and influence shouldn’t put out information automatically when the police have got a different strategy to catch and convict the wrongdoers,” Shorten said.
“I don’t want to give what Senator Hinch has done any more oxygen than that.
“For me, this is about a shocking and senseless murder. For me, it’s about the loss of a family. And the idea that your child could be lost on the other side of the world makes them particularly powerless.”
Maasarwe had been attending college on the grounds of La Trobe University, and visited a Melbourne comedy club before catching the tram home on the night of her death.
The event has sparked a series of vigils and renewed concerns about male violence.