Liban Ali, 31, is accused of killing Jayda Allen Bonner, who was found dead in the Cardigan Street complex in the Melbourne suburb of Carlton just before 2am on Saturday.
Ali was arrested early on Tuesday morning after presenting himself to a police station.
He faced Melbourne Magistrates Court on Wednesday evening after being charged with Ms Allen Bonner's murder.
Investigators believe Ali and Ms Allen Bonner were known to one another.
The 31-year-old did not speak during his brief court hearing as police sought a longer-than-usual period to compile the brief of evidence.
Lead detective Darren Bolitho told the court there was months of CCTV footage to be analysed as there were allegations of protracted violence and post-offence conduct.
There were also complexities around the autopsy and blood pattern analysis from inside the apartment, Senior Constable Bolitho said.
Magistrate Malcolm Thomas granted the longer period, accepting it was not an unusual request for homicide cases.
The magistrate also noted down Ali's custody management issues, which included previous diagnoses of post-traumatic stress disorder, anxiety and depression.
Ali did not apply for bail and was instead remanded in custody to next face court in March.
A 60-year-old man was also arrested shortly after the incident on Saturday but he was released pending further inquiries.
Flowers, photos, candles and handwritten notes have lined the entrance to the Carlton apartment block as loved ones and locals paid their respects.
A fundraiser was set up to aid funeral expenses and assist family to travel from Queensland to say their goodbyes.
"Jayda was a caring, loving young woman with a heart of gold and so much life ahead of her," Ms Allen Bonner's family wrote on the fundraiser page.
"She was deeply loved by her family and friends, and her loss has left an unimaginable void in the lives of those who knew her."
An Indigenous smoking ceremony outside a public housing tower on nearby Lygon Street will honour the Yuggera woman on Saturday evening.
Mourners will then march from the site to Parliament House to protest against gendered violence.
1800 RESPECT (1800 737 732)
Lifeline 13 11 14
Men's Referral Service 1300 766 491
13YARN 13 92 76
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