Former FHM model Reeva Steenkamp, 30, may have been mistaken for an intruder at the property in the capital Pretoria, according to local media reports.
However, the circumstances surrounding the incident were unclear. Police said the shooting early today was being treated as a murder investigation and said there had been previous incidents at the address described as "allegations of a domestic nature".
Pistorius was understood to have shot his 30-year-old girlfriend in the head and arm, although the circumstances surrounding the incident were unclear. He may have mistaken her for a burglar, the radio report said.
He will appear in court tomorrow after a planned appearance today was delayed to give the State Attorney more time to look at the case.
The 26-year-old - known as the "blade runner" - was the first double amputee to run in the Olympics.
South African police said they had arrested a 26-year-old man after a woman was shot dead at the Pretoria home of track star Pistorius.
Police spokeswoman Katlego Mogale said: "We found a nine millimetre pistol at the scene. A 26-year-old man was taken into custody."
Pistorius, who races wearing carbon fibre prosthetic blades after he was born without a fibula in both legs, was the first double amputee to run in the Olympics and reached the 400 semi-finals in London 2012.
South Africa has some of the world's highest rates of violent crime and some home-owners carry weapons to defend themselves against intruders.