The British broadcaster committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a film about the Gaza situation was the child of a Hamas representative, as determined by regulatory body Ofcom.
An probe by the media regulator into Gaza: How to Survive a Warzone has concluded that the documentary was "significantly deceptive".
The BBC's director general had earlier expressed regret, saying there had been "a serious error in relation to factual correctness".
The authority has ordered the corporation to broadcast a peak-time statement about its findings.
"Given this constitutes a major infringement of our regulations, we are instructing the corporation to transmit a message of our determinations against it on BBC2 at nine o'clock in the evening, with a date to be finalised," it said.
'Possibility to Damage Confidence'
The watchdog's statement stated: "Our probe determined that the film's omission to reveal that the voice's father occupied a role in the Hamas-administered authority was materially misleading.
"This implied that the public did not have critical information which may have been highly relevant to their assessment of the voice and the content he provided.
"Confidence is at the core of the connection between a television network and its public, particularly for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the risk to erode the exceptionally strong amounts of trust that audiences would have invested in a BBC factual programme about the conflict in Gaza."
The film was removed from iPlayer in the month of February after the narrator's family links came to light, and in July an internal BBC review concluded it infringed the broadcaster's journalistic standards on truthfulness.
A corporation official said: "The authority's determination is in agreement with the findings of the corporation's inquiry, that there was a serious error in the film in relation to the corporation's content standards on accuracy, which reflects clause 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we accept Ofcom's decision in its entirety. We will follow the penalty as soon as the date and wording are determined."
