The public service broadcaster committed a "significant breach" of industry standards by omitting to mention that the voice of a film about the Gaza conflict was the child of a Hamas official, according to British broadcasting authority Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has determined that the film was "materially misleading".
The BBC's director general had previously apologised, stating there had been "a serious error in relation to factual correctness".
The authority has directed the corporation to broadcast a peak-time statement about its decisions.
"Since this amounts to a significant violation of our code, we are instructing the broadcaster to air a message of our findings against it on the BBC's second channel at 21:00, with a timing to be determined," the regulator stated.
'Potential to Erode Confidence'
The regulator's announcement stated: "Our investigation concluded that the film's failure to disclose that the presenter's parent held a post in the Hamas-administered authority was substantially inaccurate.
"This implied that the viewers did not have critical information which may have been very significant to their judgment of the voice and the content he presented.
"Trust is at the center of the connection between a media organization and its public, especially for a public service broadcaster such as the British Broadcasting Corporation.
"This oversight had the possibility to undermine the very considerable degrees of trust that viewers would have invested in a factual film from the broadcaster about the conflict in Gaza."
The programme was withdrawn from iPlayer in the month of February after the boy's family links emerged, and in this past July an internal BBC review concluded it breached the broadcaster's journalistic standards on accuracy.
A corporation official said: "The Ofcom ruling is in line with the results of the corporation's inquiry, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on accuracy, which corresponds to regulation 2.2 of the regulator's media standards.
"We have apologised for this and we comply with the authority's determination in its entirety. We will follow the penalty as soon as the schedule and language are determined."