The public service broadcaster was found to have committed a "major breach" of media regulations by not revealing that the voice of a programme about the Gaza situation was the child of a Hamas representative, according to UK media regulator Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has determined that the programme was "significantly deceptive".
The BBC's director general had earlier expressed regret, noting there had been "a serious error in relation to truthfulness".
The regulator has ordered the BBC to air a peak-time announcement about its findings.
"As this represents a major infringement of our rules, we are directing the corporation to broadcast a statement of our findings against it on the BBC's second channel at 21:00, with a timing to be determined," the regulator stated.
'Potential to Undermine Trust'
The authority's statement declared: "The inquiry we conducted found that the documentary's failure to disclose that the narrator's parent served in a position in the Hamas-administered government was substantially inaccurate.
"This implied that the audience did not have critical information which may have been highly relevant to their judgment of the voice and the information he presented.
"Confidence is at the center of the relationship between a broadcaster and its audience, particularly for a public service broadcaster such as the British Broadcasting Corporation.
"This oversight had the possibility to undermine the significantly high degrees of confidence that viewers would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The film was removed from the BBC's streaming service in last February after the presenter's personal associations emerged, and in July an internal BBC review concluded it breached the organization's content policies on factual correctness.
A BBC spokesperson said: "The authority's determination is in agreement with the conclusions of the internal assessment, that there was a serious error in the film in relation to the broadcaster's journalistic policies on truthfulness, which reflects regulation 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with the authority's determination in its entirety. We will adhere to the penalty as soon as the timing and wording are confirmed."
