The public service broadcaster committed a "serious breach" of media regulations by not revealing that the voice of a programme about the Gaza situation was the offspring of a Hamas representative, as ruled by British broadcasting authority Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has determined that the programme was "significantly deceptive".
The BBC's director general had already issued an apology, saying there had been "a major oversight in relation to accuracy".
The authority has directed the broadcaster to transmit a prime-time announcement about its decisions.
"Given this constitutes a serious breach of our regulations, we are directing the BBC to air a message of our determinations against it on BBC Two at 21:00, with a date to be finalised," the statement read.
'Possibility to Undermine Trust'
The watchdog's report said: "The inquiry we conducted concluded that the film's omission to reveal that the narrator's parent held a position in the Hamas-administered administration was materially misleading.
"This implied that the public did not have essential details which may have been highly relevant to their evaluation of the presenter and the content he shared.
"Credibility is at the center of the bond between a media organization and its viewers, notably for a national broadcasting corporation such as the BBC.
"This oversight had the risk to erode the significantly high amounts of confidence that the public would have placed in a factual film from the broadcaster about the Gaza conflict."
The programme was withdrawn from the online platform in February after the presenter's family links emerged, and in July an broadcaster's internal assessment concluded it violated the corporation's editorial guidelines on factual correctness.
A representative for the broadcaster stated: "The Ofcom ruling is in accordance with the results of the internal assessment, that there was a significant failing in the programme in relation to the corporation's content standards on truthfulness, which corresponds to regulation 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we comply with Ofcom's decision in full. We will comply with the directive as soon as the timing and wording are determined."