The public service broadcaster engaged in a "significant breach" of media regulations by failing to disclose that the voice of a programme about the Gaza situation was the offspring of a Hamas representative, as ruled by regulatory body Ofcom.
An probe by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a serious error in relation to factual correctness".
The authority has instructed the corporation to broadcast a peak-time announcement about its findings.
"Since this amounts to a significant violation of our regulations, we are directing the corporation to transmit a message of our conclusions against it on the BBC's second channel at 21:00, with a date to be determined," it said.
'Possibility to Undermine Confidence'
The regulator's report stated: "Our probe concluded that the documentary's lack of disclosure that the presenter's male guardian occupied a post in the Hamas-run government was significantly deceptive.
"Consequently that the audience did not have critical information which may have been extremely pertinent to their assessment of the voice and the details he provided.
"Confidence is at the center of the connection between a broadcaster and its public, notably for a public service broadcaster such as the public broadcaster.
"This oversight had the possibility to undermine the very considerable levels of credibility that viewers would have put in a BBC factual programme about the conflict in Gaza."
The film was withdrawn from the BBC's streaming service in February after the presenter's family links came to light, and in July an broadcaster's internal assessment concluded it violated the broadcaster's journalistic standards on factual correctness.
A BBC spokesperson stated: "The regulator's decision is in accordance with the findings of the corporation's inquiry, that there was a major oversight in the programme in relation to the corporation's content standards on factual correctness, which aligns with clause 2.2 of the regulator's media standards.
"We have apologised for this and we comply with the authority's determination in its entirety. We will comply with the penalty as soon as the date and language are determined."
