The public service broadcaster was found to have committed a "serious breach" of broadcasting rules by failing to disclose that the presenter of a programme about Gaza was the son of a Hamas representative, as ruled by UK media regulator Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the documentary was "significantly deceptive".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a significant failing in relation to accuracy".
The authority has ordered the corporation to transmit a peak-time statement about its conclusions.
"Since this amounts to a serious breach of our regulations, we are instructing the corporation to transmit a statement of our findings against it on BBC2 at nine o'clock in the evening, with a date to be confirmed," it said.
'Possibility to Undermine Confidence'
The regulator's report said: "The inquiry we conducted found that the film's failure to disclose that the voice's male guardian occupied a position in the Hamas-controlled government was significantly deceptive.
"Consequently that the viewers did not have critical information which may have been extremely pertinent to their assessment of the voice and the content he provided.
"Credibility is at the heart of the connection between a media organization and its viewers, notably for a state-funded media outlet such as the public broadcaster.
"This error had the possibility to erode the significantly high amounts of credibility that audiences would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The documentary was pulled from iPlayer in last February after the boy's personal associations came to light, and in this past July an corporation's own inquiry found it violated the broadcaster's editorial guidelines on factual correctness.
A corporation official commented: "The regulator's decision is in accordance with the findings of the corporation's inquiry, that there was a major oversight in the film in relation to the broadcaster's journalistic policies on factual correctness, which reflects regulation 2.2 of the regulator's media standards.
"We have apologised for this and we comply with Ofcom's decision in complete. We will adhere to the penalty as soon as the date and language are confirmed."
