The British broadcaster engaged in a "significant breach" of broadcasting rules by omitting to mention that the voice of a film about Gaza was the son of a Hamas administrator, as determined by regulatory body Ofcom.
An probe by the media regulator into Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The head of the BBC had already issued an apology, saying there had been "a serious error in relation to factual correctness".
The regulator has ordered the corporation to air a prime-time statement about its findings.
"Given this constitutes a major infringement of our regulations, we are directing the broadcaster to broadcast a announcement of our conclusions against it on BBC Two at nine o'clock in the evening, with a date to be determined," it said.
'Risk to Undermine Confidence'
The authority's announcement said: "The inquiry we conducted found that the film's omission to reveal that the narrator's male guardian served in a position in the Hamas-administered government was substantially inaccurate.
"It meant that the public did not have essential details which may have been extremely pertinent to their evaluation of the presenter and the information he presented.
"Trust is at the center of the connection between a broadcaster and its viewers, especially for a national broadcasting corporation such as the British Broadcasting Corporation.
"This failing had the risk to undermine the exceptionally strong degrees of credibility that audiences would have put in a BBC factual programme about the Israel-Gaza war."
The documentary was removed from the BBC's streaming service in the month of February after the boy's personal associations were revealed, and in this past July an internal BBC review found it infringed the organization's journalistic standards on truthfulness.
A corporation official stated: "The regulator's decision is in agreement with the conclusions of the internal assessment, that there was a serious error in the documentary in relation to the broadcaster's journalistic policies on accuracy, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we comply with the authority's determination in full. We will comply with the penalty as soon as the timing and language are confirmed."
