Emergency services attended a home on Monterey St in Nollamara at about 10.30pm (AWST).
They found a 26-year-old woman who had been injured.
An ambulance took her to Royal Perth Hospital, where she later died.
During a search of the area, a police dog found a man hiding at the front of a neighbouring property.
The 40-year-old man, who police said was known to the victim, is in police custody and assisting with the investigation.