The British broadcaster engaged in a "serious breach" of media regulations by omitting to mention that the voice of a film about the Gaza situation was the son of a Hamas administrator, as determined by UK media regulator Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The BBC's director general had previously apologised, noting there had been "a significant failing in relation to truthfulness".
Ofcom has directed the broadcaster to broadcast a prime-time declaration about its conclusions.
"As this represents a significant violation of our rules, we are instructing the corporation to transmit a message of our determinations against it on BBC Two at 21:00, with a timing to be determined," the statement read.
'Possibility to Damage Trust'
The watchdog's statement said: "Our probe found that the programme's omission to reveal that the voice's father served in a post in the Hamas-controlled government was materially misleading.
"Consequently that the audience did not have essential details which may have been very significant to their judgment of the narrator and the information he presented.
"Credibility is at the center of the relationship between a broadcaster and its audience, notably for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the possibility to undermine the exceptionally strong amounts of credibility that audiences would have placed in a BBC factual programme about the conflict in Gaza."
The programme was removed from iPlayer in February after the boy's personal associations emerged, and in July an internal BBC review concluded it violated the broadcaster's journalistic standards on truthfulness.
A corporation official commented: "The Ofcom ruling is in accordance with the findings of the internal assessment, that there was a serious error in the film in relation to the broadcaster's journalistic policies on accuracy, which reflects Rule 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with the authority's determination in complete. We will follow the penalty as soon as the date and wording are finalised."