 "Paralympian Pistorius arrested for killing girlfriend")
According to the Beeld newspaper, Pistorius was arrested early Thursday following the shooting.
Police could not immediately confirm the report.
The athlete know as the "Blade Runner" made history in 2012 when he became the first amputee to compete in the Olympics.
He won gold in the 4x400m relay at the Paralympic Games.
He had both legs amputated below the knee before he was aged one, because of a congenital condition, and runs on carbon fibre blades.
Last year Time Magazine named him as one of the world's 100 most influential people.
The Johannesburg-born runner had both legs amputated below the knee when he was 11 months old after being born without lower leg bones. But he played sports unhindered while growing up, switching to running after fracturing a knee playing rugby.
At high school, he was so good that his personal fitness coach said she was unaware for six months that he ran on prosthetic legs.
But he was initially banned from competing in the Olympics in Beijing by the International Association of Athletics Federations (IAAF) on the grounds that his blades gave him an unfair advantage.
That decision was later overturned on appeal at the Court of Arbitration for Sport (CAS), although he ultimately failed to meet the Olympic qualifying standard time.
He went on to win a silver medal as part of the 4x400m relay team at the 2011 World Championships in South Korean city of Daegu before representing his country at the London Olympics and Paralympics last year.
Off the track, Pistorius is an adrenalin junkie, with a love of speed reflected in a passion for motorbikes.
Four years ago he crashed his boat in a river south of Johannesburg, breaking two ribs, an eye socket and his jaw.
He also once owned two white tigers but sold them to a zoo in Canada when they became too big.