The public service broadcaster committed a "major breach" of broadcasting rules by failing to disclose that the narrator of a film about the Gaza situation was the child of a Hamas official, as determined by regulatory body Ofcom.
An probe by the broadcasting watchdog into 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".
The authority has instructed the corporation to broadcast a evening declaration about its findings.
"Since this amounts to a significant violation of our regulations, we are ordering the broadcaster to air a statement of our conclusions against it on BBC2 at 21:00, with a schedule to be determined," the regulator stated.
The regulator's announcement said: "The inquiry we conducted determined that the film's failure to disclose that the narrator's male guardian served in a position in the Hamas-administered authority was materially misleading.
"It meant that the audience did not have critical information which may have been extremely pertinent to their judgment of the presenter and the details he provided.
"Credibility is at the core of the connection between a broadcaster and its viewers, notably for a public service broadcaster such as the public broadcaster.
"This oversight had the possibility to damage the significantly high amounts of credibility that audiences would have put in a BBC factual programme about the conflict in Gaza."
The programme was removed from iPlayer in the month of February after the boy's personal associations came to light, and in the month of July an broadcaster's internal assessment found it infringed the organization's journalistic standards on factual correctness.
A BBC spokesperson said: "The authority's determination is in accordance with the conclusions of Peter Johnston's review, that there was a serious error in the documentary in relation to the broadcaster's journalistic policies on factual correctness, which reflects Rule 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with the authority's determination in complete. We will follow the sanction as soon as the date and wording are confirmed."
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