The public service broadcaster committed a "serious breach" of industry standards by failing to disclose that the voice of a programme about Gaza was the child of a Hamas official, according to regulatory body Ofcom.
An investigation by the media regulator into the programme Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The BBC's director general had previously apologised, noting there had been "a major oversight in relation to accuracy".
Ofcom has ordered the broadcaster to air a prime-time statement about its findings.
"Since this amounts to a serious breach of our rules, we are instructing the broadcaster to air a statement of our findings against it on BBC2 at 21:00, with a timing to be finalised," it said.
'Potential to Undermine Trust'
The authority's announcement stated: "The inquiry we conducted concluded that the documentary's lack of disclosure that the voice's male guardian held a position in the Hamas-controlled government was significantly deceptive.
"Consequently that the viewers did not have essential details which may have been highly relevant to their evaluation of the voice and the details he presented.
"Credibility is at the heart of the relationship between a broadcaster and its audience, especially for a national broadcasting corporation such as the public broadcaster.
"This error had the potential to damage the exceptionally strong levels of confidence that the public would have put in a documentary produced by the BBC about the Gaza conflict."
The film was removed from iPlayer in the month of February after the narrator's familial connections emerged, and in July an corporation's own inquiry determined it infringed the corporation's content policies on truthfulness.
A corporation official stated: "The regulator's decision is in accordance with the findings of Peter Johnston's review, that there was a significant failing in the film in relation to the corporation's content standards on truthfulness, which reflects clause 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with Ofcom's decision in full. We will follow the penalty as soon as the schedule and wording are finalised."
