The public service broadcaster committed a "significant breach" of media regulations by omitting to mention that the voice of a film about the Gaza situation was the offspring of a Hamas official, as determined by regulatory body Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has determined that the programme was "significantly deceptive".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a major oversight in relation to truthfulness".
Ofcom has directed the BBC to transmit a evening declaration about its decisions.
"Given this constitutes a major infringement of our rules, we are ordering the BBC to air a statement of our determinations against it on the BBC's second channel at 21:00, with a timing to be confirmed," the statement read.
'Potential to Undermine Confidence'
The authority's statement stated: "The inquiry we conducted found that the film's omission to reveal that the voice's parent held a position in the Hamas-controlled administration was materially misleading.
"It meant that the audience did not have critical information which may have been extremely pertinent to their evaluation of the presenter and the details he presented.
"Trust is at the heart of the relationship between a media organization and its audience, notably for a public service broadcaster such as the British Broadcasting Corporation.
"This error had the possibility to erode the very considerable levels of credibility that audiences would have put in a documentary produced by the BBC about the Gaza conflict."
The documentary was withdrawn from the BBC's streaming service in February after the presenter's family links emerged, and in July an corporation's own inquiry found it breached the corporation's journalistic standards on factual correctness.
A representative for the broadcaster commented: "The regulator's decision is in agreement with the conclusions of the corporation's inquiry, that there was a serious error in the programme in relation to the corporation's content standards on truthfulness, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we comply with Ofcom's decision in its entirety. We will comply with the directive as soon as the timing and wording are confirmed."
