The footage shows Oscar Pistorius shouting and running on his stumps as he simulates holding a handgun.
It was aired in Australia only by broadcaster Channel 7 on Sunday.
A spokesperson for Oscar Pistorius’ said that the footage was filmed in order to create a “forensic animation”, but that it was “obtained illegally”.
“For the family, the airing of this footage constitutes a staggering breach of trust and an invasion of the family’s privacy,” the statement said.
The footage has not been seen in court in South Africa, where the athlete is on trial for the murder of girlfriend Reeva Steenkamp.
In the video – filmed at his uncle’s house – Oscar Pistorius rushes forwards on the stumps of his legs.
Oscar Pistorius holds out an imaginary gun in his right hand and screams: “Reeva, call the police.”
He is also shown carrying a woman out of a toilet and downstairs.
The re-enactment was done to help US specialists create a computer model of the shooting of Reeva Steenkamp.
It is not clear why the full reconstruction was not used at the murder trial.
In the leaked footage Oscar Pistorius looks unsteady on his stumps, but perhaps more mobile than one of his doctors had described in his evidence last week.
Oscar Pistorius says he shot his girlfriend after mistaking her for an intruder in their house last year.
The prosecution argues that he killed Reeva Steenkamp deliberately after a row.
Oscar Pistorius’ trial will resume on Monday, July 7.
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