The public service broadcaster was found to have committed a "major breach" of media regulations by failing to disclose that the voice of a documentary about Gaza was the child of a Hamas administrator, as determined by British broadcasting authority Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has found that the documentary was "significantly deceptive".
The chief executive of the broadcaster had already issued an apology, noting there had been "a major oversight in relation to factual correctness".
The regulator has ordered the broadcaster to transmit a prime-time declaration about its conclusions.
"As this represents a significant violation of our code, we are directing the corporation to transmit a announcement of our conclusions against it on BBC2 at 21:00, with a date to be confirmed," it said.
'Risk to Erode Credibility'
The regulator's announcement said: "Our probe determined that the documentary's lack of disclosure that the presenter's parent occupied a post in the Hamas-controlled administration was substantially inaccurate.
"This implied that the viewers did not have essential details which may have been highly relevant to their evaluation of the voice and the details he provided.
"Credibility is at the core of the connection between a media organization and its viewers, especially for a state-funded media outlet such as the BBC.
"This error had the possibility to damage the very considerable levels of trust that viewers would have put in a documentary produced by the BBC about the Israel-Gaza war."
The programme was removed from iPlayer in last February after the presenter's familial connections emerged, and in the month of July an internal BBC review concluded it infringed the broadcaster's content policies on accuracy.
A representative for the broadcaster commented: "The authority's determination is in agreement with the findings of the internal assessment, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on accuracy, which aligns with regulation 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we accept Ofcom's decision in full. We will comply with the directive as soon as the schedule and wording are finalised."