The public service broadcaster committed a "serious breach" of industry standards by failing to disclose that the voice of a programme about the Gaza situation was the son of a Hamas official, as determined by regulatory body Ofcom.
An investigation by Ofcom 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, saying there had been "a major oversight in relation to truthfulness".
The regulator has directed the corporation to air a prime-time statement about its findings.
"Since this amounts to a serious breach of our code, we are directing the BBC to air a announcement of our determinations against it on the BBC's second channel at 21:00, with a schedule to be confirmed," the statement read.
'Risk to Undermine Credibility'
The regulator's statement stated: "Our investigation determined that the documentary's failure to disclose that the voice's father held a post in the Hamas-controlled authority was substantially inaccurate.
"Consequently that the public did not have critical information which may have been extremely pertinent to their judgment of the narrator and the information he shared.
"Confidence is at the heart of the relationship between a media organization and its audience, especially for a national broadcasting corporation such as the public broadcaster.
"This oversight had the risk to erode the significantly high levels of trust that audiences would have placed in a factual film from the broadcaster about the conflict in Gaza."
The documentary was pulled from the BBC's streaming service in February after the boy's personal associations emerged, and in the month of July an corporation's own inquiry determined it breached the broadcaster's editorial guidelines on factual correctness.
A representative for the broadcaster stated: "The authority's determination is in agreement with the findings of the internal assessment, that there was a serious error in the documentary in relation to the corporation's content standards on accuracy, which reflects Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we agree with Ofcom's decision in its entirety. We will follow the penalty as soon as the date and wording are confirmed."
