The 24-year-old woman from regional Western Australia was found unresponsive in a car park at Wellington Street, near Pier Street, just before 3am.
Emergency services tried to revive the young woman but she died at the scene.
A 27-year-old man, who is also from regional WA, was arrested in Perth’s CBD a short time later and is helping police with the investigation.
Detective Senior Sergeant Keith Neubronner said the 27-year-old man and victim were known to each other and had a “domestic relationship”.
Neubronner said the woman had been assaulted but there were no obvious injuries.
He added the assault began at Yagan Square and “went all the way down to Wellington Street” where she collapsed and died.
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Neubronner said there is extensive CCTV between the two areas to show what happened and police will be collecting it today.
“We need to look at the footage and ascertain what happened,” Neubronner said.
Prior to the assault, Neubronner said there was a large group of people socialising in Yagan Square but no one saw the alleged assault of the woman.
Homicide detectives are now at the scene and have cordoned off two areas with police tape.
Anybody with information, or who has mobile phone or dashcam footage of the area between 2.30am and 3.15am, is urged to contact police.