The British broadcaster engaged in a "major breach" of broadcasting rules by failing to disclose that the narrator of a programme about Gaza was the child of a Hamas administrator, as ruled by British broadcasting authority Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the documentary was "materially misleading".
The chief executive of the broadcaster had already issued an apology, saying there had been "a serious error in relation to factual correctness".
The regulator has directed the BBC to broadcast a evening statement about its conclusions.
"Since this amounts to a major infringement of our regulations, we are instructing the BBC to transmit a statement of our determinations against it on BBC Two at nine o'clock in the evening, with a timing to be finalised," it said.
'Risk to Damage Credibility'
The regulator's statement stated: "Our probe concluded that the documentary's lack of disclosure that the voice's father held a position in the Hamas-run authority was materially misleading.
"Consequently that the viewers did not have critical information which may have been highly relevant to their judgment of the voice and the content he presented.
"Confidence is at the core of the bond between a television network and its audience, especially for a state-funded media outlet such as the public broadcaster.
"This error had the risk to erode the exceptionally strong levels of trust that the public would have invested in a factual film from the broadcaster about the Gaza conflict."
The documentary was removed from iPlayer in last February after the boy's personal associations were revealed, and in July an broadcaster's internal assessment found it violated the organization's journalistic standards on truthfulness.
A BBC spokesperson said: "The Ofcom ruling is in line with the results of the internal assessment, that there was a major oversight in the film in relation to the corporation's content standards on truthfulness, which corresponds to Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we agree with Ofcom's decision in full. We will comply with the penalty as soon as the timing and wording are finalised."