The body of Courtney Herron, 25, was found in a Melbourne park by walkers on Saturday, police said, BBC News reported.
"She died as a result of a horrendous bashing — that's the only way to describe it," said Detective Inspector Andrew Stamper.
Police have arrested a 27-year-old homeless man. Henry Hammond appeared in court on Monday charged with murder.
His lawyer told the court he had some mental health issues. Hammond was remanded in custody following his brief court appearance. His next trial hearing is in September.
Herron's death has sparked a wave of public grief and anger following a number of similar cases in Melbourne in the past year.
Her body was discovered just a short distance from another inner-city park, where comedian Eurydice Dixon was allegedly raped and killed by a stranger last June.
Police believe Herron was attacked in Royal Park in the suburb of Parkville early on Saturday, and attempts made to conceal her body.
Police described it as a ‘particularly horrendous attack’. Initial postmortem results showed no evidence of sexual assault.
Detective Inspector Stamper said Herron's family was ‘heartbroken’. Their daughter had experienced mental health and drug abuse problems and she had only ‘sporadic contact’ with her family, he said.
In recent times she was believed to have been "couch surfing with friends and possibly rough sleeping as well," said Stamper.
Addressing media on Sunday, Assistant Police Commissioner Luke Cornelius said Melbourne was a safe city but men's attitudes toward women needed to change.
"Violence against women is absolutely about men's behavior," he said.
The premier of Victoria State, Daniel Andrew, made a similar statement saying, "This is not about the way women behave... this is most likely about the behavior of men."
He has previously blamed sexist attitudes in the wake of other killings. In January, 21-year-old Israeli-Arab student Aya Maasarwe was allegedly attacked by a stranger while walking home.
The UN has said violence against women in Australia is ‘disturbingly common’, but experts say it is not an outlier among developed nations.
According to government figures, one in five women, and one in 20 men, have experienced sexual violence or threats since the age of 15.