The public service broadcaster committed a "major breach" of industry standards by omitting to mention that the presenter of a film about the Gaza conflict was the child of a Hamas official, as determined by British broadcasting authority Ofcom.
An probe by Ofcom into the documentary titled Gaza: How to Survive a Warzone has concluded that the film was "materially misleading".
The BBC's director general had earlier expressed regret, saying there had been "a serious error in relation to factual correctness".
Ofcom has ordered the corporation to air a peak-time statement about its findings.
"Given this constitutes a major infringement of our rules, we are instructing the corporation to transmit a message of our conclusions against it on the BBC's second channel at nine o'clock in the evening, with a date to be finalised," the regulator stated.
'Possibility to Erode Confidence'
The authority's announcement said: "Our investigation determined that the film's omission to reveal that the narrator's male guardian served in a role in the Hamas-controlled administration was materially misleading.
"Consequently that the public did not have vital facts which may have been very significant to their evaluation of the voice and the details he provided.
"Trust is at the center of the bond between a television network and its audience, especially for a national broadcasting corporation such as the BBC.
"This error had the potential to undermine the very considerable amounts of credibility that the public would have invested in a factual film from the broadcaster about the Israel-Gaza war."
The film was pulled from the BBC's streaming service in February after the narrator's familial connections emerged, and in the month of July an internal BBC review concluded it breached the corporation's content policies on factual correctness.
A BBC spokesperson said: "The authority's determination is in line with the conclusions 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 Ofcom's Broadcasting Code.
"We expressed regret for this and we accept the authority's determination in complete. We will follow the penalty as soon as the schedule and wording are finalised."