The public service broadcaster was found to have committed a "serious breach" of industry standards by not revealing that the narrator of a programme about the Gaza situation was the son of a Hamas representative, as ruled by regulatory body Ofcom.
An probe by the media regulator into the programme Gaza: How to Survive a Warzone has concluded that the documentary was "materially misleading".
The chief executive of the broadcaster had previously apologised, noting there had been "a serious error in relation to factual correctness".
The authority has directed the broadcaster to broadcast a peak-time announcement about its conclusions.
"Since this amounts to a serious breach of our code, we are directing the broadcaster to air a announcement of our findings against it on BBC2 at 21:00, with a timing to be finalised," the regulator stated.
The authority's announcement stated: "Our probe concluded that the film's omission to reveal that the voice's father occupied a post in the Hamas-administered authority was substantially inaccurate.
"Consequently that the viewers did not have critical information which may have been extremely pertinent to their judgment of the narrator and the content he presented.
"Trust is at the heart of the bond between a media organization and its public, particularly for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the possibility to damage the very considerable amounts of confidence that the public would have put in a documentary produced by the BBC about the Israel-Gaza war."
The documentary was pulled from the BBC's streaming service in February after the presenter's familial connections emerged, and in July an corporation's own inquiry determined it violated the broadcaster's content policies on accuracy.
A BBC spokesperson stated: "The regulator's decision is in line with the conclusions of the corporation's inquiry, that there was a significant failing in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which aligns with Rule 2.2 of the regulator's media standards.
"We expressed regret for this and we accept the regulator's ruling in full. We will adhere to the penalty as soon as the schedule and wording are determined."
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