The public service broadcaster was found to have committed a "major breach" of broadcasting rules by failing to disclose that the presenter of a documentary about the Gaza conflict was the offspring of a Hamas representative, according to regulatory body Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The head of the BBC had already issued an apology, saying there had been "a major oversight in relation to truthfulness".
The regulator has instructed the corporation to air a peak-time announcement about its findings.
"As this represents a major infringement of our code, we are ordering the BBC to broadcast a statement of our findings against it on BBC2 at 21:00, with a schedule to be determined," it said.
'Risk to Erode Credibility'
The authority's report declared: "Our investigation determined that the film's lack of disclosure that the narrator's parent held a post in the Hamas-controlled administration was substantially inaccurate.
"It meant that the public did not have critical information which may have been extremely pertinent to their assessment of the narrator and the details he shared.
"Credibility is at the heart of the relationship between a media organization and its public, particularly for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the risk to damage the very considerable amounts of trust that viewers would have placed in a BBC factual programme about the conflict in Gaza."
The film was pulled from the BBC's streaming service in the month of February after the boy's personal associations came to light, and in the month of July an internal BBC review concluded it infringed the broadcaster's editorial guidelines on truthfulness.
A representative for the broadcaster said: "The regulator's decision is in agreement with the findings of Peter Johnston's review, that there was a significant failing in the film in relation to the corporation's content standards on truthfulness, which corresponds to clause 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we accept the authority's determination in full. We will adhere to the penalty as soon as the date and language are finalised."