Police said a 26-year-old man, who they have not named, was in custody and a case of murder was being investigated.
The precise circumstances surrounding the incident are unclear. Reports say he may have mistaken her for a burglar.
Oscar 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 in court later on Thursday, reports say.
The news that he may have killed his girlfriend will shock the country as Oscar Pistorius is regarded as one of South Africa’s national icons.
The incident is said to have taken place between 04:00 and 05:00 local time.
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.
Reeva Steenkamp had been wounded in her head and upper body. Paramedics were at the house when police arrived, but she died at the scene. A 9 mm pistol was recovered.
Police gave no further details about the woman’s alleged relationship with Oscar Pistorius.
Reeva Steenkamp, 30, a former FHM model who has been dating Oscar Pistorius for two months.
South Africa has among the highest rates of crime in the world and many residents keep weapons to protect themselves against intruders.
But the country also has a careful vetting process before awarding gun licences, said Erika Gibson of Beeld newspaper.
Oscar 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 400 m semi-finals in the London 2012 Olympics. At the Paralympics he won silver in the T44 200 m, gold in the 4×100 relay and gold in the T44 400 m, setting a Paralympic record.
For years he dominated in his category at successive Paralympic Games.
In 2008 Oscar Pistorius won a legal battle over his blades with the International Association of Athletics Federations (IAAF) for the right to compete in able-bodied competitions.
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.
The International Paralympic Committee also declined to comment on the matter as a police investigation was under way.
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