The British broadcaster was found to have committed a "significant breach" of media regulations by omitting to mention that the presenter of a programme about the Gaza situation was the offspring of a Hamas administrator, as ruled by UK media regulator Ofcom.
An investigation by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The BBC's director general had already issued an apology, saying there had been "a serious error in relation to truthfulness".
The regulator has ordered the broadcaster to transmit a peak-time statement about its findings.
"Given this constitutes a serious breach of our code, we are instructing the BBC to broadcast a announcement of our findings against it on BBC Two at nine o'clock in the evening, with a date to be confirmed," the statement read.
'Possibility to Erode Confidence'
The authority's announcement declared: "Our investigation determined that the film's failure to disclose that the voice's parent held a role in the Hamas-administered government was significantly deceptive.
"Consequently that the viewers did not have essential details which may have been very significant to their evaluation of the voice and the information he provided.
"Trust is at the core of the bond between a media organization and its viewers, notably for a national broadcasting corporation such as the BBC.
"This oversight had the potential to damage the very considerable degrees of trust that viewers would have invested in a BBC factual programme about the Israel-Gaza war."
The film was pulled from the BBC's streaming service in February after the boy's personal associations were revealed, and in July an broadcaster's internal assessment found it breached the broadcaster's content policies on factual correctness.
A BBC spokesperson stated: "The authority's determination is in line with the findings of the internal assessment, that there was a significant failing in the film in relation to the broadcaster's journalistic policies on truthfulness, which aligns with regulation 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we agree with the regulator's ruling in its entirety. We will comply with the penalty as soon as the schedule and language are determined."