The public service broadcaster was found to have committed a "significant breach" of media regulations by omitting to mention that the voice of a film about Gaza was the child of a Hamas administrator, according to UK media regulator Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The chief executive of the broadcaster had already issued an apology, noting there had been "a serious error in relation to accuracy".
Ofcom has ordered the corporation to air a peak-time statement about its conclusions.
"As this represents a significant violation of our code, we are directing the corporation to broadcast a statement of our findings against it on BBC Two at nine o'clock in the evening, with a timing to be finalised," it said.
'Possibility to Erode Credibility'
The authority's announcement stated: "Our investigation concluded that the programme's lack of disclosure that the presenter's father held a role in the Hamas-controlled government was materially misleading.
"Consequently that the public did not have vital facts which may have been extremely pertinent to their evaluation of the presenter and the content he presented.
"Credibility is at the heart of the connection between a broadcaster and its viewers, especially for a public service broadcaster such as the British Broadcasting Corporation.
"This oversight had the risk to undermine the very considerable levels of trust that audiences would have invested in a documentary produced by the BBC about the Gaza conflict."
The film was withdrawn from the online platform in the month of February after the boy's family links were revealed, and in the month of July an broadcaster's internal assessment concluded it infringed the organization's editorial guidelines on factual correctness.
A BBC spokesperson commented: "The Ofcom ruling is in accordance 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 accuracy, which corresponds to regulation 2.2 of Ofcom's Broadcasting Code.
"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 date and wording are determined."
