The British broadcaster was found to have committed a "serious breach" of industry standards by not revealing that the voice of a programme about the Gaza situation was the child of a Hamas official, as ruled by regulatory body Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The BBC's director general had earlier expressed regret, saying there had been "a serious error in relation to truthfulness".
The regulator has directed the broadcaster to air a prime-time statement about its conclusions.
"As this represents a major infringement of our regulations, we are ordering the broadcaster to broadcast a message of our conclusions against it on BBC2 at 9pm, with a date to be determined," it said.
'Risk to Erode Credibility'
The authority's report declared: "The inquiry we conducted found that the programme's omission to reveal that the presenter's parent held a post in the Hamas-run authority was significantly deceptive.
"It meant that the viewers did not have vital facts which may have been very significant to their evaluation of the voice and the content he presented.
"Credibility is at the core of the relationship between a television network and its audience, particularly for a public service broadcaster such as the British Broadcasting Corporation.
"This oversight had the potential to erode the exceptionally strong degrees of trust that audiences would have placed in a documentary produced by the BBC about the Gaza conflict."
The documentary was pulled from the BBC's streaming service in the month of February after the narrator's family links emerged, and in July an broadcaster's internal assessment found it violated the organization's editorial guidelines on accuracy.
A corporation official said: "The authority's determination is in accordance with the conclusions of Peter Johnston's review, that there was a serious error in the film in relation to the BBC's Editorial Guidelines on accuracy, which reflects Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we accept Ofcom's decision in full. We will comply with the directive as soon as the schedule and wording are determined."
