The public service broadcaster was found to have committed a "major breach" of media regulations by not revealing that the voice of a programme about the Gaza conflict was the son of a Hamas official, as ruled by regulatory body Ofcom.
An investigation by Ofcom into Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a serious error in relation to truthfulness".
The regulator has instructed the broadcaster to broadcast a peak-time announcement about its decisions.
"Since this amounts to a significant violation of our rules, we are instructing the BBC to transmit a message of our findings against it on the BBC's second channel at 21:00, with a schedule to be confirmed," the statement read.
'Potential to Damage Credibility'
The regulator's statement stated: "The inquiry we conducted found that the programme's omission to reveal that the narrator's parent served in a position in the Hamas-administered administration was substantially inaccurate.
"This implied that the public did not have essential details which may have been extremely pertinent to their assessment of the narrator and the details he presented.
"Trust is at the core of the bond between a media organization and its viewers, particularly for a public service broadcaster such as the public broadcaster.
"This oversight had the risk to damage the exceptionally strong levels of confidence that audiences would have placed in a factual film from the broadcaster about the conflict in Gaza."
The programme was pulled from the online platform in February after the boy's family links emerged, and in July an internal BBC review concluded it infringed the broadcaster's editorial guidelines on factual correctness.
A corporation official said: "The regulator's decision is in agreement with the conclusions of Peter Johnston's review, that there was a significant failing in the film in relation to the corporation's content standards on accuracy, which corresponds to regulation 2.2 of the regulator's media standards.
"We have apologised for this and we accept the authority's determination in its entirety. We will follow the directive as soon as the timing and wording are finalised."
