Scott Allen Miller, 42, was arrested on the New South Wales far south coast andtaken to Eden police station on Monday about 3.30pm.
His apprehension followed the discovery by joggers on Saturday morning of the naked body of a 32-year-old Chinese woman in Melbourne's Kings Domain.
Although still to be formally identified, police believe she was a hospitality employee and on her way to work about 5.30am that morning.
Homicide Squad Detective Inspector John Potter confirmed on Monday that the woman had been sexually assaulted before she died.
"This is a particularly violent assault on this woman, she has been sexually assaulted and she has been physically assaulted," Insp Potter said.
Police say CCTV footage shows the victim being chased by a man while crossing St Kilda Road before disappearing in the vicinity of the Police Memorial about 5.30am.
Detectives have been in touch with her family in China to confirm her identity.
They have also released footage of a man they believe to be Miller walking down Swanston Street, near the Town Hall, talking to another man just before 2am on Saturday.
Inspector Potter said detectives also wanted to speak to the man seen speaking to Miller but did not regard him as a suspect.
The two walked into a pub in Bourke Street about 1.55am and Miller is seen on the video leaving alone about 5am.
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