The public service broadcaster engaged in a "serious breach" of media regulations by not revealing that the voice of a documentary about the Gaza situation was the son of a Hamas administrator, as ruled by regulatory body Ofcom.
An investigation by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a serious error in relation to truthfulness".
The authority has ordered the corporation to air a peak-time declaration about its findings.
"Given this constitutes a significant violation of our code, we are ordering the BBC to broadcast a statement of our findings against it on BBC2 at nine o'clock in the evening, with a timing to be confirmed," it said.
'Risk to Erode Confidence'
The watchdog's announcement said: "Our investigation concluded that the programme's failure to disclose that the voice's parent served in a post in the Hamas-run government was significantly deceptive.
"This implied that the audience did not have critical information which may have been highly relevant to their assessment of the narrator and the information he provided.
"Credibility is at the heart of the bond between a media organization and its public, notably for a state-funded media outlet such as the public broadcaster.
"This oversight had the risk to damage the very considerable levels of trust that viewers would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The programme was pulled from iPlayer in February after the presenter's family links were revealed, and in the month of July an broadcaster's internal assessment concluded it violated the organization's editorial guidelines on factual correctness.
A representative for the broadcaster said: "The regulator's decision is in accordance with the findings of the internal assessment, that there was a significant failing in the film in relation to the BBC's Editorial Guidelines on truthfulness, which aligns with Rule 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we agree with the regulator's ruling in full. We will follow the directive as soon as the date and wording are determined."
