The public service broadcaster committed a "major breach" of media regulations by failing to disclose that the narrator of a film about the Gaza situation was the son of a Hamas representative, as determined by UK media regulator Ofcom.
An inquiry by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the film was "substantially inaccurate".
The BBC's director general had earlier expressed regret, noting there had been "a serious error in relation to truthfulness".
The regulator has ordered the BBC to broadcast a prime-time announcement about its decisions.
"Given this constitutes a major infringement of our rules, we are directing the BBC to transmit a statement of our determinations against it on the BBC's second channel at 21:00, with a timing to be confirmed," it said.
The authority's report stated: "Our probe concluded that the documentary's lack of disclosure that the presenter's parent held a position in the Hamas-run government was substantially inaccurate.
"It meant that the public did not have essential details which may have been extremely pertinent to their evaluation of the voice and the information he provided.
"Credibility 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 risk to undermine the very considerable levels of credibility that viewers would have placed in a BBC factual programme about the Gaza conflict."
The documentary was removed from the BBC's streaming service in February after the boy's personal associations were revealed, and in this past July an internal BBC review concluded it infringed the organization's journalistic standards on accuracy.
A representative for the broadcaster said: "The authority's determination is in agreement with the conclusions of Peter Johnston's review, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on factual correctness, which corresponds to clause 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we agree with the regulator's ruling in its entirety. We will follow the penalty as soon as the date and wording are finalised."
Elena Marchetti is a technology journalist with a passion for demystifying complex topics. She has been covering tech trends for over a decade.