The public service broadcaster committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a film about the Gaza situation was the child of a Hamas administrator, according to regulatory body Ofcom.
An probe by the media regulator into the documentary titled Gaza: How to Survive a Warzone has found that the documentary was "significantly deceptive".
The head of the BBC had already issued an apology, saying there had been "a serious error in relation to factual correctness".
The authority has instructed the corporation to air a evening announcement about its conclusions.
"Given this constitutes a significant violation of our code, we are instructing the BBC to air a message of our determinations against it on the BBC's second channel at nine o'clock in the evening, with a schedule to be determined," it said.
'Potential to Undermine Credibility'
The watchdog's announcement stated: "Our investigation found that the documentary's lack of disclosure that the presenter's father occupied a role in the Hamas-administered administration was materially misleading.
"It meant that the public did not have critical information which may have been highly relevant to their evaluation of the presenter and the information he provided.
"Trust is at the core of the bond between a broadcaster and its audience, especially for a public service broadcaster such as the public broadcaster.
"This failing had the potential to damage the exceptionally strong levels of trust that the public would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was pulled from the BBC's streaming service in the month of February after the boy's family links were revealed, and in July an corporation's own inquiry found it breached the corporation's content policies on accuracy.
A corporation official commented: "The authority's determination is in accordance with the findings of the internal assessment, that there was a serious error in the film in relation to the corporation's content standards on truthfulness, which aligns with clause 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we accept the authority's determination in complete. We will adhere to the directive as soon as the date and wording are finalised."