The British broadcaster was found to have committed a "major breach" of broadcasting rules by failing to disclose that the voice of a programme about Gaza was the child of a Hamas official, as determined by British broadcasting authority Ofcom.
An inquiry by the media regulator into the programme Gaza: How to Survive a Warzone has concluded that the programme was "materially misleading".
The chief executive of the broadcaster had previously apologised, saying there had been "a significant failing in relation to factual correctness".
The regulator has ordered the BBC to transmit a peak-time declaration about its findings.
"Since this amounts to a serious breach of our regulations, we are instructing the broadcaster to air a statement of our determinations against it on the BBC's second channel at 9pm, with a timing to be confirmed," the regulator stated.
'Possibility to Erode Credibility'
The authority's announcement stated: "Our probe concluded that the programme's omission to reveal that the narrator's father held a post in the Hamas-administered government was materially misleading.
"It meant that the audience did not have vital facts which may have been highly relevant to their evaluation of the voice and the details he provided.
"Trust is at the core of the bond between a television network and its public, particularly for a national broadcasting corporation such as the public broadcaster.
"This oversight had the possibility to erode the very considerable amounts of credibility that audiences would have placed in a documentary produced by the BBC about the conflict in Gaza."
The programme was withdrawn from iPlayer in February after the narrator's familial connections emerged, and in July an corporation's own inquiry concluded it violated the corporation's editorial guidelines on accuracy.
A corporation official said: "The regulator's decision is in agreement with the results of Peter Johnston's review, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on accuracy, which reflects clause 2.2 of the regulator's media standards.
"We issued an apology for this and we accept Ofcom's decision in full. We will adhere to the directive as soon as the timing and wording are determined."