The British broadcaster engaged in a "serious breach" of industry standards by not revealing that the voice of a film about the Gaza situation was the offspring of a Hamas administrator, as ruled by regulatory body Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The chief executive of the broadcaster had already issued an apology, noting there had been "a serious error in relation to accuracy".
The authority has ordered the BBC to transmit a prime-time statement about its decisions.
"Given this constitutes a serious breach of our code, we are ordering the broadcaster to broadcast 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 confirmed," the statement read.
'Possibility to Erode Confidence'
The regulator's announcement declared: "Our investigation found that the film's failure to disclose that the narrator's parent occupied a post in the Hamas-run authority was materially misleading.
"This implied that the audience did not have vital facts which may have been extremely pertinent to their evaluation of the narrator and the content he presented.
"Credibility is at the center of the bond between a media organization and its viewers, especially for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the possibility to damage the exceptionally strong amounts of credibility that viewers would have put in a BBC factual programme about the Israel-Gaza war."
The documentary was removed from iPlayer in last February after the boy's family links emerged, and in the month of July an internal BBC review determined it breached the broadcaster's content policies on factual correctness.
A representative for the broadcaster stated: "The Ofcom ruling is in agreement with the results of the corporation's inquiry, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on factual correctness, which corresponds to Rule 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we agree with the regulator's ruling in complete. We will adhere to the penalty as soon as the schedule and language are confirmed."