Gauteng Police said that a 26-year-old-man had been arrested and was being questioned.
South African media have named the 30-year-old victim as Pistorius' girlfriend Reeva Steenkamp. She was allegedly shot dead in the early hours of Thursday morning at the sprinter's home in Pretoria.
The precise circumstances surrounding the incident are unclear but Beeld newspaper reported on its website that Pistorius accidentally shot Steenkamp after mistaking her for a robber.
"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 that Pistorius was the shooter.
"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."
The incident is said to have taken place between 4am and 5am local time and the suspect is set to appear in court later today.
"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," Mogale added.
A 9mm pistol was recovered was recovered from the scene.
Pistorius is one of South Africa's national icons and was born without a fibula in both legs.
For years he has dominated in his category at Paralympic Games.
He races wearing carbon fibre prosthetic "blades" and reached the 400m semi-finals in the London 2012 Olympics.
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