Police were called to the house in the early hours of the morning, where they found paramedics treating a 29-year-old woman with gunshot wounds to the head and upper body. She died at the scene.
Officers have recovered a 9mm pistol.
A 26-year-old man will appear in court on Friday.
Early reports said Mr Pistorius might have mistaken his girlfriend for an intruder at his home in the upmarket Silver Woods gated compound on the outskirts of South Africa's administrative capital.
Oscar Pistorius
Popularly known as "blade runner", he was born without a fibula in both legs
Won a key legal battle in 2008, when athletics' governing body, the IAAF, allowed him to compete against able-bodied athletes
Made history in London 2012 by becoming the first amputee sprinter to compete in the Olympics
Apologised after claiming that his rival, Brazilian Alan Oliveira, was wearing blades that were too long in the 2012 Paralympics 200m final
However, police say neighbours heard screaming and shouting around the time of the shooting, and that they had been called to investigate incidents of a domestic nature at the same house in the past.
They also said that they would oppose any bail application.
Mr Pistorius, 26, was the first double amputee to run in the Olympics.
Known as the "blade runner", Mr Pistorius races wearing carbon fibre prosthetic blades after he was born without a fibula in both legs and had his legs amputated below the knee before his first birthday.
For years he dominated in his category at successive Paralympic Games, but 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.
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.
Sarit Tomlinson, Reeva Steenkamp's publicist, described her client as "an absolute angel"
Miss Steenkamp's publicist confirmed to the BBC that the 29-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.
Ed Warner, head of UK Athletics, described the developments as "shocking and very sad," adding: "Pistorius is one of the great icons of Paralympic athletics but also of able-bodied athletics too."
South Africa has one of the highest rates of crime in the world and many residents keep weapons to protect themselves against intruders.
But gun ownership is strictly regulated and it is not easy to obtain a licence.
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.
