The public service broadcaster engaged in a "serious breach" of broadcasting rules by not revealing that the voice of a documentary about Gaza was the offspring of a Hamas representative, as determined by UK media regulator Ofcom.
An probe by the broadcasting watchdog into Gaza: How to Survive a Warzone has determined that the programme was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, stating there had been "a major oversight in relation to truthfulness".
The authority has instructed the broadcaster to transmit a prime-time declaration about its findings.
"Given this constitutes a serious breach of our code, we are directing the broadcaster to air a statement of our determinations against it on the BBC's second channel at 21:00, with a timing to be determined," it said.
'Possibility to Damage Credibility'
The regulator's report said: "Our probe concluded that the documentary's lack of disclosure that the voice's parent held a role in the Hamas-administered administration was substantially inaccurate.
"This implied that the public did not have essential details which may have been extremely pertinent to their evaluation of the presenter and the details he provided.
"Credibility is at the heart of the bond between a broadcaster and its audience, notably for a state-funded media outlet such as the public broadcaster.
"This error had the possibility to damage the significantly high levels of confidence that the public would have invested in a documentary produced by the BBC about the Israel-Gaza war."
The documentary was withdrawn from the online platform in last February after the boy's personal associations emerged, and in July an broadcaster's internal assessment concluded it breached the organization's editorial guidelines on accuracy.
A representative for the broadcaster said: "The authority's determination is in line with the findings of Peter Johnston's review, that there was a major oversight in the film in relation to the corporation's content standards on factual correctness, which corresponds to Rule 2.2 of the regulator's media standards.
"We expressed regret for this and we accept Ofcom's decision in full. We will follow the directive as soon as the timing and wording are finalised."