Police say they arrived at a home in Sydney's inner west within one minute of receiving a triple-zero call just after 11am on Thursday.
When officers attended the Russell Lea property, they found a woman aged in her 50s dead with several stab wounds to her upper body.
The 42-year-old arrested at the scene was one of five residents at the home, investigators say. 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.
The man and the woman, who is yet to be formally identified, were not thought to be in an intimate relationship, she added.
The 42-year-old had no criminal history of violence and only had 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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