Mr Pistorius's girlfriend is being named in local media as 30-year-old model, Reeva Steenkamp.
South African Paralympic athlete Oscar Pistorius has been arrested over the fatal shooting of his girlfriend Reeva Steenkamp at his home, local media say.
Police said they have charged a 26-year-old man with murder, but did not confirm it was Mr Pistorius.
The precise circumstances surrounding the incident are unclear. Reports say he may have mistaken her for a burglar.
Mr Pistorius, 26, is known as the "blade runner", and was the first double amputee to run in the Olympics.
The suspect is expected to appear at Pretoria Magistrates' Court later on Thursday, police said.
They also confirmed that a woman had been shot dead at the home of Oscar Pistorius and that she was a friend of the athlete.
Police added that there had been previous incidents at the address and described them as "allegations of a domestic nature".
"The SA Police Service were just as surprised this morning to hear on the radio that allegations had been made that the deceased had been perceived to be a burglar," police spokesperson Denise Beuke said, adding that they were not the source of those allegations.
Reeva Steenkamp's publicist confirmed to the BBC that the 30-year-old model had died.
"Everyone who knew her is in tears. She was an absolute angel, the sweetest, sweetest human being, a kind human being," Sarit Tomlinson said.
The news that Mr Pistorius may have killed his girlfriend will shock the country as the athlete is regarded as one of South Africa's national icons, reports the BBC's Peter Biles from Cape Town.
The incident is said to have taken place between 04:00 and 05:00 local time (02:00-03:00 GMT).
A police statement said that a 30-year-old woman was "fatally wounded" in the early hours of Thursday morning at a home in the Silverlakes complex in the Boschkop area of the capital.
The woman had been wounded in her head and upper body. Paramedics were at the house when police arrived, but she died at the scene. A 9mm pistol was recovered.
South Africa has among the highest rates of crime in the world and many residents keep weapons to protect themselves against intruders.
Gun ownership is strictly regulated and obtaining a licence can take years due to bureaucratic red tape.
On Tuesday, a bill seeking to give police extra powers to arrest anyone carrying a dangerous weapon in public was tabled before parliament, following a spate of violent strikes and protests last year.
The athlete's home is in a high-security up-market gated compound on the outskirts of Pretoria.
Reporters have gathered outside the estate but police have not let anybody inside, local television reports.
Mr Pistorius races wearing carbon fibre prosthetic blades after he was born without a fibula in both legs and had both legs amputated below the knee before his first birthday.
He reached the 400m semi-finals in the London 2012 Olympics. At the Paralympics he won silver in the T44 200m, gold in the 4x100 relay and gold in the T44 400m, setting a Paralympic record.
For years he dominated in his category at successive Paralympic Games.
In 2008 he won a legal battle over his blades with the International Association of Athletics Federations (IAAF) for the right to compete in able-bodied competitions. Icon of athletics
His achievements have made him a "living legend" and placed him among global sporting royalty, South African broadcaster and commentator Daniel Silke told the BBC.
"He's a household name, he's a hero in the South African sporting context. He is of course someone who has overcome great difficulty and tragedy in his own personal life," he added.
The South African Sports Confederation and Olympic Committee said it had been inundated with questions over the incident, but was in no position to comment.
Ed Warner, head of UK Athletics also reiterated that little was known about the incident but described the reports as "shocking and very sad," adding that: "Pistorius is one of the great icons of Paralympic athletics but also of able-bodied athletics too".
The International Paralympic Committee also declined to comment on the matter as a police investigation was under way.