The British broadcaster committed a "serious breach" of media regulations by omitting to mention that the presenter of a film about the Gaza situation was the son of a Hamas administrator, as ruled by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has concluded that the film was "substantially inaccurate".
The BBC's director general had previously apologised, saying there had been "a significant failing in relation to accuracy".
The authority has ordered the broadcaster to air a peak-time declaration about its conclusions.
"Since this amounts to a major infringement of our rules, we are directing the BBC to transmit a statement of our conclusions against it on BBC Two at nine o'clock in the evening, with a schedule to be finalised," the statement read.
'Risk to Erode Credibility'
The regulator's report said: "Our probe found that the documentary's lack of disclosure that the narrator's parent served in a role in the Hamas-administered government was substantially inaccurate.
"Consequently that the viewers did not have critical information which may have been very significant to their evaluation of the presenter and the details he presented.
"Trust is at the heart of the connection between a broadcaster and its public, especially for a state-funded media outlet such as the BBC.
"This oversight had the potential to undermine the very considerable amounts of confidence that the public would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The programme was removed from the BBC's streaming service in February after the boy's personal associations were revealed, and in July an corporation's own inquiry found it violated the broadcaster's content policies on truthfulness.
A BBC spokesperson commented: "The regulator's decision is in accordance with the conclusions of the corporation's inquiry, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on accuracy, which reflects clause 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we accept the authority's determination in full. We will adhere to the directive as soon as the date and wording are confirmed."