The public service broadcaster engaged in a "serious breach" of media regulations by omitting to mention that the presenter of a film about the Gaza conflict was the offspring of a Hamas official, according to regulatory body Ofcom.
An inquiry by Ofcom into Gaza: How to Survive a Warzone has concluded that the film was "significantly deceptive".
The head of the BBC had previously apologised, saying there had been "a significant failing in relation to factual correctness".
The authority has directed the broadcaster to transmit a evening statement about its findings.
"Given this constitutes a major infringement of our rules, we are instructing the corporation to air a message of our conclusions against it on BBC2 at 9pm, with a date to be confirmed," the statement read.
'Possibility to Undermine Trust'
The regulator's announcement declared: "Our probe found that the film's lack of disclosure that the voice's parent served in a position in the Hamas-controlled government was substantially inaccurate.
"Consequently that the public did not have critical information which may have been highly relevant to their judgment of the narrator and the content he presented.
"Credibility is at the core of the connection between a broadcaster and its public, especially for a national broadcasting corporation such as the public broadcaster.
"This error had the possibility to damage the exceptionally strong degrees of trust that the public would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was withdrawn from the BBC's streaming service in February after the boy's family links emerged, and in the month of July an internal BBC review determined it violated the corporation's editorial guidelines on accuracy.
A BBC spokesperson said: "The authority's determination is in agreement with the results of the corporation's inquiry, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which aligns with regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we accept Ofcom's decision in its entirety. We will comply with the sanction as soon as the date and wording are confirmed."