Police were called to a home in the suburb of Floreat on Friday afternoon after reports of gunshots.
Detectives said a 63-year-old man arrived at the property about 4.30pm looking for his former partner who was not there at the time.
Instead, the man shot dead a 59-year-old woman who was his ex-partner's friend and critically wounded her 18-year-old daughter, police said.
He then took his own life.
Police arrived to find the two bodies, and paramedics rushed the 18-year-old girl to Royal Perth Hospital where she later died.
WA Police Detective Inspector David Gorton said officers had arrived on the street by the time the last shot was fired.
"We believe that last shot was the male taking his own life," he told reporters on Saturday.
"We still have ballistic technicians at the scene (and) at this stage, we're really unsure about how many shots were fired."
The mother was a close friend of the shooter's ex-wife.
Det Insp Gorton said the man was known to police but did not have a history of violence.
"Any death is tragic," he said.
"However, when you get a multiple murder, it has that greater impact on the family, the friends, the first responders and certainly the community at large."
Police declared a crime scene at the property and said there was no ongoing threat to the public.
Det Insp Gorton said police were continuing to support the man's ex-wife, family, friends and emergency responders affected by the tragic incident.
"We had the ex-wife and one of her daughters in our care at homicide squad last night (and) we are providing any support we can to them," he said.
"Obviously they are very distressed by these circumstances and WA Police will make the appropriate referrals to them for counselling."
However, police are not treating the shooting as family violence-related because the man and the mother were not in a relationship, despite having met on previous occasions.
The investigation into the circumstances of the shooting is ongoing.
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