The video, made by US company The Evidence Room and commissioned by Pistorius' defence team, was shown by the Seven Network's Sunday Night.
Footage shows Pistorius, charged with murdering his girlfriend Reeva Steenkamp on February 14 last year, walking on his stumps with his hand clenched as if he were ready to fire a gun.
The reenactment was a summary of Pistorius' version of events as he has told a court during his trial, which is ongoing.
His cries and screams were part of the reenactment.
In a statement, Brian Webber said Pistorius' defence team engaged the services of The Evidence Room in October 2013.
"The company was engaged to visually map the events on the night of the accident. As part of this process, certain video footage was filmed," he said.
"The “visual mapping” was for trial preparation only and was not intended to be used for any other purpose."
Webber said the footage had been "obtained illegally and in breach of the non-disclosure agreement with The Evidence Room".
"Its usage also constitutes a breach of privilege as this material was produced for trial purposes on the instructions of a commissioner, and the ownership of the copyright vests in the commissioner. No permission for the disclosure thereof has been given," he said.
"For the family, the airing of this footage constitutes a staggering breach of trust and an invasion of the family's privacy.
"It has come to our attention that Channel 7 purchased this footage unlawfully. In addition, during our engagement with Channel 7, we received an undertaking that they would not air any of the material before the end of the trial.
"Whilst we cannot imagine how any of the footage would not support Oscar’s version, we will only be in a position to comment further once we have had the opportunity to study what has been aired."
Sunday Night executive producer Mark Llewellyn denied suggestions the footage was obtained illegally.
"The material shown on Sunday Night goes to the heart of both the prosecution and defence cases, including the account provided by Oscar Pistorius," Llewellyn said in a statement.
"We would not have run the footage if we thought we had obtained it illegally. The story was run in Australia only and not made available to any other territory."
Pistorius has always maintained his innocence, insisting he did not deliberately shoot Steenkamp.