The public service broadcaster was found to have committed a "serious breach" of media regulations by failing to disclose that the narrator of a programme about Gaza was the son of a Hamas representative, as determined by regulatory body Ofcom.
An probe by the broadcasting watchdog into the documentary titled Gaza: How to Survive a Warzone has found that the programme was "significantly deceptive".
The head of the BBC had earlier expressed regret, saying there had been "a major oversight in relation to factual correctness".
Ofcom has ordered the broadcaster to transmit a peak-time declaration about its findings.
"Since this amounts to a major infringement of our rules, we are ordering the corporation to air a message of our conclusions against it on BBC2 at 21:00, with a date to be confirmed," the statement read.
'Possibility to Erode Confidence'
The watchdog's statement stated: "The inquiry we conducted found that the documentary's omission to reveal that the presenter's father held a role in the Hamas-administered authority was significantly deceptive.
"It meant that the audience did not have critical information which may have been extremely pertinent to their judgment of the voice and the content he presented.
"Trust is at the center of the relationship between a broadcaster and its public, especially for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the possibility to damage the exceptionally strong amounts of confidence that the public would have placed in a BBC factual programme about the conflict in Gaza."
The film was withdrawn from the BBC's streaming service in February after the boy's family links were revealed, and in July an internal BBC review found it infringed the broadcaster's journalistic standards on truthfulness.
A corporation official said: "The regulator's decision is in agreement with the results 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 corresponds to Rule 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we comply with the regulator's ruling in complete. We will comply with the penalty as soon as the schedule and wording are determined."
