The public service broadcaster committed a "major breach" of media regulations by not revealing that the voice of a programme about Gaza was the son of a Hamas representative, according to regulatory body Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has concluded that the documentary was "materially misleading".
The head of the BBC had already issued an apology, stating there had been "a serious error in relation to factual correctness".
The authority has instructed the broadcaster to broadcast a peak-time declaration about its conclusions.
"Given this constitutes a serious breach of our regulations, we are instructing the corporation to transmit a announcement of our determinations against it on the BBC's second channel at 9pm, with a timing to be confirmed," the regulator stated.
'Possibility to Erode Credibility'
The authority's announcement said: "Our investigation found that the film's omission to reveal that the voice's father held a position in the Hamas-controlled government was substantially inaccurate.
"This implied that the audience did not have vital facts which may have been extremely pertinent to their evaluation of the voice and the information he provided.
"Trust is at the heart of the bond between a broadcaster and its viewers, notably for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the potential to undermine the exceptionally strong levels of credibility that audiences would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The film was withdrawn from the BBC's streaming service in the month of February after the narrator's family links came to light, and in this past July an corporation's own inquiry concluded it breached the broadcaster's content policies on factual correctness.
A corporation official commented: "The regulator's decision is in agreement with the findings of Peter Johnston's review, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on accuracy, which aligns with regulation 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we comply with Ofcom's decision in full. We will adhere to the penalty as soon as the schedule and language are determined."
