The man, 27, of no fixed address, was arrested on Sunday and charged overnight with one count of murder and will appear in Melbourne Magistrates Court on Monday, Victoria Police said in a statement.

The battered body of Ms Herron, 25, was found by dog walkers in Royal Park in the inner Melbourne suburb of Parkville on Saturday morning.

Police said she had suffered extreme violence.

"This was a particularly, particularly horrendous attack," Homicide squad Detective Inspector Andrew Stamper said on Sunday.

Ms Herron had been couch surfing and sleeping rough for some time while struggling with drug and mental health issues.

Insp Stamper said she had been in sporadic contact with her family and there were "a lot of people out there who knew and loved Courtney".

"When there's a child that suffered drug use, mental health issues, family relationships can be fragmented," he said.

"That doesn't mean that families out there don't love their children, and you know, our heart breaks for them.

"We are dealing with a heartbroken family again."

Ms Herron's killing has sent shock waves among the wider Melbourne community with prominent and everyday Victorians outraged over the death of yet another young woman.

Over the weekend friends of Ms Herron and others her laid floral tributes at the site where her body was found - just a short distance from Princes Park, where the body of aspiring comedian Eurydice Dixon was found on June 12 last year.

Ms Dixon, 22, was raped and murdered. Aiia Maasarwe, 21, also died after being attacked while walking home near La Trobe University on January 15.

Both women were attacked by men they did not know and who have since been charged.

Then in April, Natalina Angok's body was found dumped in Chinatown, allegedly killed by her one-time partner Christopher Allen who has since been charged.

The last confirmed sighting of Ms Herron was on May 14 at St Albans when she came into contact with the police.

Australian Associated Press