The public service broadcaster was found to have committed a "major breach" of industry standards by omitting to mention that the voice of a programme about Gaza was the child of a Hamas official, according to UK media regulator Ofcom.
An investigation by Ofcom into Gaza: How to Survive a Warzone has found that the documentary was "significantly deceptive".
The BBC's director general had previously apologised, saying there had been "a serious error in relation to truthfulness".
Ofcom has instructed the corporation to broadcast a evening statement about its findings.
"Since this amounts to a major infringement of our regulations, we are directing the BBC to transmit a statement of our conclusions against it on the BBC's second channel at 21:00, with a date to be determined," it said.
'Possibility to Undermine Confidence'
The regulator's announcement declared: "The inquiry we conducted found that the documentary's omission to reveal that the narrator's parent occupied a post in the Hamas-controlled authority was substantially inaccurate.
"Consequently that the audience did not have critical information which may have been very significant to their judgment of the narrator and the information he presented.
"Confidence is at the core of the relationship between a media organization and its public, especially for a public service broadcaster such as the public broadcaster.
"This failing had the potential to erode the exceptionally strong degrees of trust that the public would have put in a factual film from the broadcaster about the Israel-Gaza war."
The film was withdrawn from iPlayer in the month of February after the narrator's personal associations were revealed, and in July an internal BBC review determined it violated the corporation's content policies on accuracy.
A corporation official commented: "The regulator's decision is in agreement with the findings of Peter Johnston's review, that there was a significant failing in the film in relation to the broadcaster's journalistic policies on truthfulness, which aligns with clause 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we agree with the authority's determination in full. We will comply with the penalty as soon as the timing and wording are finalised."
