The public service broadcaster was found to have committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a film about the Gaza situation was the son of a Hamas representative, as ruled by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The BBC's director general had previously apologised, saying there had been "a serious error in relation to accuracy".
Ofcom has directed the BBC to transmit a prime-time declaration about its findings.
"Since this amounts to a major infringement of our regulations, we are ordering the broadcaster to transmit a statement of our findings against it on BBC Two at 9pm, with a timing to be finalised," it said.
'Potential to Damage Credibility'
The authority's announcement said: "The inquiry we conducted concluded that the documentary's failure to disclose that the narrator's parent held a post in the Hamas-controlled authority was materially misleading.
"Consequently that the public did not have critical information which may have been highly relevant to their assessment of the narrator and the information he shared.
"Confidence is at the heart of the relationship between a media organization and its viewers, notably for a state-funded media outlet such as the BBC.
"This failing had the potential to undermine the very considerable levels of credibility that audiences would have put in a documentary produced by the BBC about the Israel-Gaza war."
The film was pulled from the online platform in February after the presenter's family links emerged, and in July an broadcaster's internal assessment concluded it violated the organization's journalistic standards on factual correctness.
A representative for the broadcaster stated: "The authority's determination is in accordance with the findings of the internal assessment, that there was a serious error in the programme in relation to the corporation's content standards on accuracy, which corresponds to clause 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we comply with the regulator's ruling in full. We will adhere to the directive as soon as the timing and language are finalised."
