The public service broadcaster was found to have committed a "major breach" of media regulations by failing to disclose that the voice of a film about Gaza was the offspring of a Hamas administrator, according to British broadcasting authority Ofcom.
An probe by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the film was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a significant failing in relation to truthfulness".
The regulator has directed the corporation to air a evening announcement about its decisions.
"Since this amounts to a significant violation of our rules, we are ordering the BBC to broadcast a statement of our determinations against it on the BBC's second channel at 21:00, with a date to be confirmed," the statement read.
'Possibility to Erode Credibility'
The watchdog's statement said: "Our probe found that the programme's failure to disclose that the presenter's male guardian served in a post in the Hamas-administered administration was significantly deceptive.
"It meant that the public did not have vital facts which may have been extremely pertinent to their evaluation of the narrator and the content he provided.
"Trust is at the heart of the bond between a broadcaster and its viewers, particularly for a state-funded media outlet such as the public broadcaster.
"This failing had the possibility to damage the exceptionally strong amounts of credibility that viewers would have placed in a BBC factual programme about the conflict in Gaza."
The film was removed from the BBC's streaming service in February after the boy's personal associations came to light, and in July an broadcaster's internal assessment determined it violated the organization's journalistic standards on truthfulness.
A corporation official commented: "The authority's determination is in agreement with the findings of the internal assessment, that there was a major oversight in the film in relation to the broadcaster's journalistic policies on accuracy, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we agree with the regulator's ruling in complete. We will comply with the sanction as soon as the schedule and language are confirmed."