A high-speed chase through the Cape Flats ended in a gunfight after a car rammed pursuing traffic co.
The 26-year-old, has been arrested for the shooting.
"I can confirm to you that a 26-year-old suspect will be appearing in the Pretoria Magistrate's Court this afternoon following a shooting at Oscar Pistorius' house," spokeswoman Lt-Col Katlego Mogale said.
"Paramedics declared the woman dead on the scene and police proceeded with their investigation. The woman sustained wounds to her head and the upper body," spokeswoman Lt-Col Katlego Mogale said.
Mogale would not confirm an earlier news report that Pistorius was the shooter.
The woman shot dead had been identified as model Reeva Steenkamp, 30.
Shiri Reouveni, of Steenkamp's PR agency, said they had been told it was Steenkamp who had been shot, but did not want to say more.
Asked if she could confirm if it was Steenkamp who was shot, she said: "Yes".
Mogale said police were called following a shooting at a townhouse complex in Silverlakes.
"When police arrived they found the paramedics attending to the woman. The paramedics declared the woman dead on the scene and police proceeded with their investigation of the scene."
A 9mm pistol was recovered.
The man has been taken into custody and a case of murder was being investigated.