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.