The woman, aged in her 50s, was found inside the home in Sydney's inner west and had only been living at the property for a few weeks.
Police said they received a triple-zero call from a concerned neighbour just after 11am, arriving at the Russell Lea address within minutes.Â
Inside, they found the woman with significant stab wounds to her upper body.
A 42-year-old man was arrested at the scene as police continue to investigate the domestic-violence death.
He was one of five residents at the home, investigators said. All occupants were present when the alleged attack took place.
"We know that the victim and the other housemates moved into this residence five to six weeks ago," Superintendent Christine McDonald told reporters on Thursday.
The man and the woman, who is yet to be formally identified, were not thought to be in an intimate relationship, she added.
The man had no criminal history of violence, with minor traffic and drug offences on his record.
He has not been charged, but was talking to investigators at Burwood police station on Thursday.
The man moved into the residence around three weeks after the woman, Supt McDonald said.
"The fact that they are living together, residing albeit for two to three weeks, makes it a domestic-violence incident," she said.
The other three residents of the share house are providing statements to investigators.
Police are asking for anyone with information to come forward.
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