The public service broadcaster committed a "significant breach" of media regulations by failing to disclose that the narrator of a programme about Gaza was the offspring of a Hamas administrator, as ruled by regulatory body Ofcom.
An probe by the media regulator into Gaza: How to Survive a Warzone has concluded that the film was "materially misleading".
The chief executive of the broadcaster had already issued an apology, stating there had been "a significant failing in relation to accuracy".
Ofcom has directed the BBC to broadcast a peak-time announcement about its conclusions.
"Given this constitutes a serious breach of our code, we are ordering the broadcaster to air a announcement of our findings against it on BBC2 at 9pm, with a timing to be finalised," the regulator stated.
'Potential to Erode Trust'
The watchdog's report stated: "The inquiry we conducted found that the programme's lack of disclosure that the narrator's parent occupied a position in the Hamas-run authority was substantially inaccurate.
"This implied that the viewers did not have critical information which may have been very significant to their assessment of the presenter and the details he provided.
"Trust is at the heart of the relationship between a media organization and its viewers, particularly for a public service broadcaster such as the British Broadcasting Corporation.
"This error had the risk to undermine the very considerable levels of trust that the public would have put in a factual film from the broadcaster about the conflict in Gaza."
The film was removed from the BBC's streaming service in February after the boy's family links were revealed, and in July an broadcaster's internal assessment concluded it infringed the organization's journalistic standards on truthfulness.
A representative for the broadcaster said: "The regulator's decision is in line with the conclusions of Peter Johnston's review, that there was a significant failing in the film in relation to the corporation's content standards on accuracy, which reflects clause 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we agree with the regulator's ruling in complete. We will adhere to the penalty as soon as the date and wording are determined."