A 27-year-old man has appeared in court charged with what police describe as a "horrendous bashing" murder of a woman whose body was found in a major Melbourne park.

Key points: Henry Hammond, 27, made a brief appearance in the Melbourne Magistrates' Court and was remanded in custody

Henry Hammond, 27, made a brief appearance in the Melbourne Magistrates' Court and was remanded in custody Magistrate Donna Bakos ordered a medical assessment after the court was told he may have a "delusional disorder"

Magistrate Donna Bakos ordered a medical assessment after the court was told he may have a "delusional disorder" Police earlier said Ms Herron had been couch surfing and her family was "heartbroken"

Courtney Herron, 25, was found dead by dogwalkers near a pile of logs in Royal Park, in Parkville just north of the CBD, about 9:25am on Saturday.

Henry Hammond was arrested and interviewed on Sunday, and homicide squad detectives charged him with one count of murder overnight.

Mr Hammond, 27 and of no fixed address, made a brief appearance at the Melbourne Magistrates' Court this morning and was remanded in custody until September.

The court heard Mr Hammond may have autism and a "delusional disorder".

He had been diagnosed with attention deficit hyperactivity disorder (ADHD) and prescribed an array of medications to treat it, the court was told.

Magistrate Donna Bakos ordered a medical assessment be conducted as soon as possible.

Floral tributes were left where Ms Herron's body was found. ( ABC News: Zalika Rizmal )

Mr Hammond, wearing a black tracksuit top, occasionally smiled at people in the court gallery before returning his attention to the magistrate.

Lawyer Bernie Balmer, who appeared on behalf of Mr Hammond, said outside the court it was a "complicated and tragic situation".

Police believe Ms Herron, who was homeless, was attacked in the park on Friday night or Saturday morning.

They said it was not clear whether a weapon was used and there was no evidence that she had been sexually assaulted.

'A heartbroken family'

Detective Inspector Andrew Stamper said Ms Herron had experienced issues with drugs and mental illness and had been couch surfing.

He said she might have been sleeping rough but it was not clear whether she had been sleeping in the park.

Police said Ms Herron had only "sporadic" contact with family. ( Supplied: Victoria Police )

She was last seen on May 14 in St Albans, in Melbourne's west, when she had contact with police.

Detectives were trying to retrace her steps since then.

Inspector Stamper said Ms Herron had lived a "fairly transient lifestyle" and only had "sporadic" contact with her family.

"Family relationships can be fragmented, but I stress that doesn't mean families out there don't love their children," he said on Sunday.

"We're dealing with a heartbroken family here."

A GoFundMe fundraising webpage has been set up by the Melbourne Homeless Collective for donations for Ms Herron's family to put towards funeral costs.

Police have stepped up patrols in the park and members of the public left floral tributes at the spot where Ms Herron was found.

"You deserved so much better. May you rest in everlasting peace," one note read.

Victorian Premier Daniel Andrews called Ms Herron's death a "terrible, terrible tragedy" and said the Government would make any changes Victoria Police might recommend to improve public safety.

Challenging attitudes

Melburnians are reeling from a series of unrelated killings of women by men.

In several recent cases, the victims' bodies have been discovered in parks and other public places by passers-by.

Phil Cleary, an anti-violence campaigner whose sister was killed by her ex-partner, said there were complex social factors behind violence against women.

Ms Herron's body was found near a pile of logs on Saturday morning. ( AAP: James Ross )

"It's a fundamental contradiction that we have here between the assertion of men's rights and women trying to find their rights in the aftermath of second-wave feminism," he told ABC Radio Melbourne.

"What men are grappling with is their loss of power."

The Council to Homeless Persons said homeless women were particularly at risk of violence.

"We can protect women like Courtney, but as a society have to choose to do it and it's a choice that Victoria can and should make," CEO Jenny Smith said in a statement.

"There are far too few housing options that women on low incomes can afford, and crisis accommodation and refuges are full of people who can't move on to permanent housing, because the affordable options just aren't there."

Last week, the Victorian Government committed to build 1,000 units of public housing by 2022.

Jacqui Watt, the CEO of the group No to Violence, said more needed to be done to challenge attitudes towards women.

"At No to Violence, we've been at this for 25 years," she told ABC Radio Melbourne.

"We have to start work much earlier with many more agents of change, if you like — start in schools, start in communities.

"As the police and Premier said, this is a man's problem so we've got to see real resources to enable us to tackle this."