The video was produced by an American company apparently hired by the athlete's lawyers, but has not been used during his trial in South Africa.
In the video, Pistorius is seen running on his stumps with his right arm held out, seeming to imitate holding a gun.
In another shot he is seen carrying a woman from the bathroom.
His legal team have said they are taking action against Channel Seven in Australia, which has been broadcasting a trailer of the video before showing it on its current affairs programme Sunday Night. The video has not been broadcast anywhere except Australia, but clips have also been shown in South African television news reports about the footage.
Pistorius's attorney Brian Webber said: "We are busy taking action against the Australian media house [that has the video].
"They have no right to broadcast the video. We will deal with it accordingly."
The footage could be seen as significant because it appears to show the athlete, a double amputee, running on his stumps with a "fair amount of movement".
Defence witnesses have argued that his movement on his stumps is extremely limited.
The leak comes just a week after the runner's murder trial resumed following a break for psychiatric evaluation, which concluded Pistorius could be held criminally responsible if found guilty.
Prosecutors claim the athlete shot 29-year-old model Ms Steenkamp in cold blood, but Pistorius has insisted he fired in self-defence believing that an intruder was hiding in the bathroom.