The public service broadcaster was found to have committed a "serious breach" of broadcasting rules by not revealing that the voice of a film about the Gaza conflict was the offspring of a Hamas representative, according to UK media regulator Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The chief executive of the broadcaster had earlier expressed regret, stating there had been "a serious error in relation to factual correctness".
The authority has ordered the broadcaster to broadcast a prime-time declaration about its decisions.
"Given this constitutes a major infringement of our regulations, we are ordering the BBC to transmit a statement of our determinations against it on BBC Two at 21:00, with a date to be confirmed," the regulator stated.
'Potential to Undermine Confidence'
The authority's statement stated: "Our probe concluded that the programme's omission to reveal that the presenter's male guardian held a post in the Hamas-controlled administration was substantially inaccurate.
"This implied that the viewers did not have essential details which may have been extremely pertinent to their judgment of the voice and the information he presented.
"Trust is at the heart of the relationship between a television network and its public, notably for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the possibility to undermine the significantly high degrees of confidence that audiences would have put in a factual film from the broadcaster about the conflict in Gaza."
The programme was removed from the BBC's streaming service in February after the boy's familial connections were revealed, and in July an corporation's own inquiry concluded it violated the broadcaster's editorial guidelines on truthfulness.
A corporation official stated: "The authority's determination is in line with the findings of the corporation's inquiry, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on truthfulness, which reflects Rule 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with Ofcom's decision in full. We will adhere to the penalty as soon as the schedule and wording are confirmed."