The public service broadcaster engaged in a "serious breach" of broadcasting rules 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 Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The chief executive of the broadcaster had previously apologised, saying there had been "a significant failing in relation to factual correctness".
The authority has ordered the BBC to transmit a peak-time statement about its findings.
"As this represents a significant violation of our regulations, we are ordering the corporation to broadcast a announcement of our determinations against it on BBC2 at 21:00, with a schedule to be confirmed," it said.
'Potential to Damage Credibility'
The regulator's announcement said: "The inquiry we conducted found that the documentary's failure to disclose that the voice's male guardian held a role in the Hamas-controlled administration was significantly deceptive.
"This implied that the viewers did not have vital facts which may have been highly relevant to their assessment of the voice and the content he presented.
"Credibility is at the core of the connection between a media organization and its viewers, especially for a state-funded media outlet such as the BBC.
"This error had the potential to erode the significantly high degrees of trust that the public would have put in a BBC factual programme about the Israel-Gaza war."
The film was withdrawn from the BBC's streaming service in last February after the boy's family links emerged, and in July an broadcaster's internal assessment determined it infringed the organization's journalistic standards on factual correctness.
A corporation official commented: "The authority's determination is in accordance with the findings of Peter Johnston's review, that there was a major oversight in the film 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 accept Ofcom's decision in full. We will adhere to the penalty as soon as the date and language are finalised."
