The public service broadcaster committed a "significant breach" of broadcasting rules by not revealing that the presenter of a documentary about the Gaza situation was the offspring of a Hamas official, as ruled by regulatory body Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has concluded that the programme was "substantially inaccurate".
The chief executive of the broadcaster had already issued an apology, stating there had been "a serious error in relation to truthfulness".
The authority has directed the corporation to transmit a peak-time announcement about its decisions.
"Since this amounts to a serious breach of our regulations, we are instructing the corporation to transmit a message of our conclusions against it on the BBC's second channel at 21:00, with a date to be confirmed," it said.
'Possibility to Damage Credibility'
The regulator's statement stated: "Our investigation concluded that the film's lack of disclosure that the narrator's male guardian held a role in the Hamas-administered government was substantially inaccurate.
"It meant that the viewers did not have essential details which may have been highly relevant to their judgment of the narrator and the information he presented.
"Credibility is at the core of the relationship between a television network and its public, notably for a national broadcasting corporation such as the BBC.
"This oversight had the potential to damage the exceptionally strong amounts of confidence that audiences would have invested in a documentary produced by the BBC about the conflict in Gaza."
The programme was withdrawn from the BBC's streaming service in February after the boy's familial connections came to light, and in July an broadcaster's internal assessment determined it breached the broadcaster's editorial guidelines on accuracy.
A corporation official said: "The authority's determination 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 aligns with regulation 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 follow the directive as soon as the schedule and wording are finalised."