The public service broadcaster engaged in a "major breach" of media regulations by not revealing that the voice of a programme about Gaza was the son of a Hamas official, as determined by UK media regulator Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has concluded that the documentary was "significantly deceptive".
The chief executive of the broadcaster had already issued an apology, saying there had been "a significant failing in relation to truthfulness".
The authority has instructed the corporation to air a evening declaration about its findings.
"As this represents a serious breach of our code, we are directing the broadcaster to broadcast a statement of our findings against it on BBC2 at nine o'clock in the evening, with a schedule to be confirmed," it said.
'Risk to Undermine Trust'
The authority's report said: "Our probe concluded that the film's lack of disclosure that the voice's male guardian served in a post in the Hamas-controlled authority was significantly deceptive.
"Consequently that the public did not have vital facts which may have been very significant to their evaluation of the narrator and the content he provided.
"Trust is at the core of the bond between a media organization and its public, especially for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the potential to erode the exceptionally strong degrees of credibility that viewers would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The film was removed from the online platform in February after the presenter's family links came to light, and in July an broadcaster's internal assessment concluded it violated the corporation's editorial guidelines on truthfulness.
A BBC spokesperson said: "The authority's determination is in agreement with the results of the corporation's inquiry, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on factual correctness, which reflects regulation 2.2 of the regulator's media standards.
"We issued an apology for this and we comply with the authority's determination in complete. We will comply with the sanction as soon as the timing and language are finalised."
