The public service broadcaster committed a "serious breach" of broadcasting rules by failing to disclose that the voice of a film about the Gaza situation was the child of a Hamas official, as determined by regulatory body Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has found that the documentary was "significantly deceptive".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a significant failing in relation to accuracy".
The regulator has ordered the BBC to transmit a evening declaration about its decisions.
"Given this constitutes a major infringement of our code, we are directing the broadcaster to transmit a statement of our conclusions against it on BBC Two at 21:00, with a timing to be confirmed," the statement read.
'Possibility to Erode Confidence'
The watchdog's report said: "Our investigation found that the film's lack of disclosure that the voice's male guardian occupied a post in the Hamas-controlled administration was significantly deceptive.
"Consequently that the audience did not have critical information which may have been extremely pertinent to their assessment of the narrator and the content he presented.
"Credibility is at the core of the bond between a media organization and its audience, especially for a national broadcasting corporation such as the British Broadcasting Corporation.
"This error had the possibility to erode the significantly high degrees of trust that the public would have put in a BBC factual programme about the Gaza conflict."
The documentary was withdrawn from iPlayer in last February after the presenter's personal associations were revealed, and in July an broadcaster's internal assessment determined it breached the organization's editorial guidelines on accuracy.
A corporation official said: "The regulator's decision is in line with the results of the internal assessment, that there was a serious error in the film in relation to the broadcaster's journalistic policies on truthfulness, which aligns with Rule 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with the regulator's ruling in full. We will comply with the sanction as soon as the timing and wording are determined."
