The 26-year-old - known as the Blade Runner - is reported to have shot Reeva Steenkamp in the arm and head at his home in Pretoria, South Africa.
Speculation in local suggests Pistorius may have been mistaken Steenkamp for a burglar.
A spokeswoman for Pretoria police said: "A 26-year-old man has been taken into custody. The incident happened at 3am. We received a call and attended the scene.
"The call did not come from the man in custody but from another person. Currently there is an inquiry into what happened."
Officers found a 9-mm pistol at the scene and took the 26-year-old Pistorius into custody. He is expected to appear in court on 14 February.
South Africa's Sports Confederation and Olympic committee have issued a statement saying they are not in a position to comment about the shooting.
A spokesperson said: "SASCOC, like the rest of the public, knows no more than what is in the public domain, which is there has been an alleged fatal shooting on the basis of a mistaken identity and an apparent assumption of a burglary.
"The organization is in no position to comment on the incident other than to say our deepest sympathy and condolences have been expressed to the families of all concerned."
The International Paralympic Committee added: "The IPC would like to offer its deepest sympathy and condolences to all families involved in this case."
Pistorius, who wears carbon fibre prosthetic blades to race, made history last year when he became the first double amputee to run in both the Olympics and Paralympic games, competing in the 400m and 4x400m relay.
The Johannesburg-born athlete who was born without fibulas in his legs and had the limbs amputated below the knee when he was 11 months old.
He won a legal battle with the International Association of Athletics Federations (IAAF) in 2008 for the right to compete in able-bodied competitions.
Update: Oscar Pistorius Charged with Murder
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