Courtney Herron, 25, was found dead by dog walkers in Royal Park at Parkville on Saturday morning with injuries described by police as "horrendous".

Police arrested Henry Richard Hammond, 27, on Sunday and he faced Melbourne Magistrates Court on Monday on a single charge of murder.

Ms Herron had been couch surfing and sleeping rough while struggling with drug and mental health issues at the time of her death.

Hammond also has no fixed address.

"It's a very tragic and complex situation," his lawyer Bernie Balmer said outside court after Hammond's brief appearance.

He told magistrate Donna Bakos that Hammond had a number of issues that would affect him in custody.

"There's a diagnosis of possible delusional disorder, possible autism spectrum disorder and historical diagnosis of ADHD," Mr Balmer said.

Hammond has previously taken medication to treat those conditions, including an anti-psychotic prescription.

The magistrate ordered that he undergo a medical assessment.

Dressed in black, and without shoes, Hammond said nothing during the short court appearance.

With one black eye, he looked around the courtroom, sometimes smiling.

Prosecutor Madeleine Sargent originally asked for up to four months for police to compile their brief of evidence against Hammond.

A pathology report is still to be completed and officers are reviewing CCTV footage, she said.

Ms Bakos gave police until August 5 to prepare the documents and ordered that Hammond be remanded in custody until a committal mention on September 16.

Lifeline 13 11 14

beyondblue 1300 22 4636

Australian Associated Press