The public service broadcaster committed a "significant breach" of media regulations by omitting to mention that the voice of a film about Gaza was the offspring of a Hamas administrator, as ruled by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The head of the BBC had earlier expressed regret, stating there had been "a serious error in relation to truthfulness".
The authority has directed the corporation to broadcast a prime-time declaration about its conclusions.
"Given this constitutes a major infringement of our rules, we are instructing the BBC to air a statement of our determinations against it on the BBC's second channel at nine o'clock in the evening, with a schedule to be finalised," it said.
'Risk to Erode Confidence'
The regulator's report declared: "The inquiry we conducted found that the film's omission to reveal that the voice's parent held a role in the Hamas-controlled administration was materially misleading.
"Consequently that the viewers did not have critical information which may have been highly relevant to their assessment of the narrator and the information he provided.
"Confidence is at the core of the bond between a broadcaster and its audience, especially for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the risk to erode the significantly high amounts of credibility that the public would have invested in a factual film from the broadcaster about the conflict in Gaza."
The documentary was removed from iPlayer in last February after the boy's personal associations were revealed, and in the month of July an broadcaster's internal assessment found it violated the organization's journalistic standards on accuracy.
A corporation official said: "The authority's determination is in line with the findings of Peter Johnston's review, that there was a major oversight in the film in relation to the broadcaster's journalistic policies on truthfulness, which aligns with regulation 2.2 of the regulator's media standards.
"We expressed regret for this and we accept the regulator's ruling in full. We will follow the penalty as soon as the schedule and wording are confirmed."
