The British broadcaster was found to have committed a "significant breach" of industry standards by failing to disclose that the narrator of a programme about Gaza was the offspring of a Hamas official, according to UK media regulator Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The head of the BBC had earlier expressed regret, saying there had been "a serious error in relation to factual correctness".
The regulator has ordered the corporation to transmit a prime-time declaration about its findings.
"As this represents a major infringement of our regulations, we are ordering the corporation to transmit a statement of our determinations against it on BBC Two at nine o'clock in the evening, with a date to be finalised," the statement read.
'Possibility to Damage Credibility'
The authority's report stated: "Our investigation determined that the programme's lack of disclosure that the presenter's male guardian occupied a position in the Hamas-run administration was substantially inaccurate.
"Consequently that the viewers did not have vital facts which may have been very significant to their judgment of the voice and the information he provided.
"Credibility is at the core of the connection between a media organization and its public, notably for a national broadcasting corporation such as the BBC.
"This error had the possibility to erode the significantly high levels of trust that the public would have placed in a documentary produced by the BBC about the conflict in Gaza."
The documentary was removed from the BBC's streaming service in February after the boy's personal associations came to light, and in the month of July an internal BBC review concluded it violated the organization's content policies on factual correctness.
A corporation official commented: "The Ofcom ruling is in line with the results of the internal assessment, that there was a serious error in the documentary in relation to the broadcaster's journalistic policies on truthfulness, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we agree with Ofcom's decision in complete. We will comply with the penalty as soon as the date and wording are finalised."
