The British broadcaster engaged in a "significant breach" of broadcasting rules by failing to disclose that the presenter of a programme about Gaza was the child of a Hamas official, according to regulatory body Ofcom.
An probe by the media regulator into the documentary titled Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The head of the BBC had previously apologised, stating there had been "a serious error in relation to truthfulness".
Ofcom has instructed the BBC to broadcast a peak-time statement about its conclusions.
"As this represents a serious breach of our regulations, we are ordering the broadcaster to transmit a announcement of our conclusions against it on the BBC's second channel at 9pm, with a date to be determined," it said.
The regulator's report stated: "The inquiry we conducted found that the programme's omission to reveal that the narrator's parent held a position in the Hamas-controlled authority was materially misleading.
"This implied that the viewers did not have vital facts which may have been very significant to their evaluation of the presenter and the information he presented.
"Credibility is at the heart of the bond between a media organization and its audience, particularly for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the risk to damage the significantly high degrees of credibility that the public would have placed in a documentary produced by the BBC about the Gaza conflict."
The documentary was withdrawn from iPlayer in last February after the boy's family links were revealed, and in July an corporation's own inquiry found it infringed the broadcaster's journalistic standards on truthfulness.
A representative for the broadcaster said: "The regulator's decision 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 reflects 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 follow the penalty as soon as the date and wording are confirmed."
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