The British broadcaster was found to have committed a "significant breach" of industry standards by omitting to mention that the narrator of a film about the Gaza conflict was the offspring of a Hamas representative, as ruled by British broadcasting authority Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the programme was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a major oversight in relation to factual correctness".
The authority has instructed the corporation to transmit a peak-time declaration about its findings.
"As this represents a serious breach of our code, we are directing the BBC to broadcast a statement of our findings against it on BBC Two at 21:00, with a schedule to be determined," it said.
'Risk to Undermine Credibility'
The authority's report stated: "Our investigation found that the documentary's failure to disclose that the voice's parent served in a position in the Hamas-run administration was materially misleading.
"This implied that the public did not have vital facts which may have been highly relevant to their evaluation of the presenter and the information he shared.
"Confidence is at the core of the bond between a media organization and its public, notably for a national broadcasting corporation such as the British Broadcasting Corporation.
"This failing had the potential to damage the very considerable amounts of confidence that viewers would have put in a BBC factual programme about the Gaza conflict."
The programme was withdrawn from iPlayer in February after the presenter's family links emerged, and in July an internal BBC review found it violated the broadcaster's editorial guidelines on accuracy.
A corporation official said: "The regulator's decision is in agreement with the findings of the internal assessment, that there was a major oversight in the film in relation to the corporation's content standards on accuracy, which reflects Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we agree with the regulator's ruling in its entirety. We will adhere to the sanction as soon as the date and language are finalised."
