The public service broadcaster committed a "serious breach" of broadcasting rules by omitting to mention that the narrator of a programme about the Gaza situation was the child of a Hamas official, as determined by British broadcasting authority Ofcom.
An inquiry by the media regulator into the documentary titled Gaza: How to Survive a Warzone has found that the documentary was "substantially inaccurate".
The chief executive of the broadcaster had already issued an apology, saying there had been "a major oversight in relation to truthfulness".
The authority has ordered the broadcaster to transmit a peak-time announcement about its conclusions.
"Given this constitutes a serious breach of our code, we are instructing the broadcaster to broadcast a statement of our findings against it on BBC2 at 21:00, with a schedule to be confirmed," it said.
'Risk to Erode Credibility'
The authority's statement declared: "Our probe determined that the film's omission to reveal that the presenter's father occupied a role in the Hamas-administered authority was materially misleading.
"This implied that the public did not have essential details which may have been highly relevant to their judgment of the narrator and the information he provided.
"Confidence is at the heart of the relationship between a television network and its public, particularly for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the possibility to damage the very considerable degrees of credibility that audiences would have placed in a BBC factual programme about the Gaza conflict."
The programme was withdrawn from the BBC's streaming service in February after the boy's familial connections emerged, and in July an broadcaster's internal assessment determined it infringed the corporation's editorial guidelines on truthfulness.
A representative for the broadcaster stated: "The authority's determination is in accordance with the conclusions of Peter Johnston's review, that there was a significant failing in the programme in relation to the corporation's content standards on factual correctness, which aligns with clause 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we agree with the regulator's ruling in full. We will adhere to the penalty as soon as the schedule and language are determined."