The British broadcaster was found to have committed a "serious breach" of broadcasting rules by failing to disclose that the voice of a film about Gaza was the offspring of a Hamas administrator, as determined by regulatory body Ofcom.
An investigation by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a significant failing in relation to factual correctness".
The authority has directed the broadcaster to air a peak-time announcement about its findings.
"Since this amounts to a significant violation of our regulations, we are instructing the broadcaster to transmit a statement of our determinations against it on the BBC's second channel at 9pm, with a date to be finalised," the statement read.
'Potential to Undermine Trust'
The authority's statement said: "Our probe determined that the documentary's failure to disclose that the voice's male guardian occupied a post in the Hamas-run administration was significantly deceptive.
"This implied that the public did not have critical information which may have been very significant to their assessment of the voice and the details he presented.
"Confidence is at the heart of the bond between a media organization and its audience, notably for a national broadcasting corporation such as the British Broadcasting Corporation.
"This failing had the risk to damage the exceptionally strong degrees of trust that the public would have put in a factual film from the broadcaster about the conflict in Gaza."
The film was withdrawn from iPlayer in February after the boy's family links came to light, and in July an broadcaster's internal assessment found it infringed the organization's journalistic standards on factual correctness.
A BBC spokesperson said: "The regulator's decision is in agreement with the results of the corporation's inquiry, that there was a serious error in the programme in relation to the broadcaster's journalistic policies on factual correctness, which corresponds to clause 2.2 of the regulator's media standards.
"We issued an apology for this and we comply with the regulator's ruling in its entirety. We will follow the penalty as soon as the timing and wording are finalised."
