The public service broadcaster engaged in a "significant breach" of media regulations by omitting to mention that the presenter of a programme about Gaza 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 concluded that the film was "significantly deceptive".
The head of the BBC had previously apologised, saying there had been "a significant failing in relation to accuracy".
The regulator has ordered the broadcaster to transmit a prime-time declaration about its findings.
"Since this amounts to a significant violation of our rules, we are ordering the broadcaster to air a message of our findings against it on BBC Two at nine o'clock in the evening, with a schedule to be determined," the regulator stated.
'Risk to Undermine Credibility'
The regulator's announcement declared: "Our probe concluded that the documentary's lack of disclosure that the voice's father served in a role in the Hamas-administered authority was significantly deceptive.
"This implied that the public did not have vital facts which may have been very significant to their evaluation of the presenter and the details he provided.
"Confidence is at the core of the bond between a television network and its public, particularly for a public service broadcaster such as the British Broadcasting Corporation.
"This error had the possibility to damage the exceptionally strong levels of confidence that the public would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The film was withdrawn from the BBC's streaming service in the month of February after the presenter's familial connections came to light, and in July an broadcaster's internal assessment concluded it breached the broadcaster's editorial guidelines on factual correctness.
A representative for the broadcaster said: "The authority's determination is in agreement with the conclusions of the corporation's inquiry, that there was a serious error in the film in relation to the broadcaster's journalistic policies on accuracy, which reflects Rule 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we comply with the regulator's ruling in its entirety. We will comply with the penalty as soon as the schedule and language are finalised."
