The public service broadcaster committed a "significant breach" of broadcasting rules by not revealing that the presenter of a documentary about the Gaza situation was the offspring of a Hamas representative, as determined by regulatory body Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the programme was "materially misleading".
The BBC's director general had previously apologised, noting there had been "a significant failing in relation to factual correctness".
The regulator has ordered the broadcaster to broadcast a evening declaration about its conclusions.
"As this represents a significant violation of our code, we are instructing the BBC to air 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 confirmed," it said.
The watchdog's report said: "Our probe concluded that the documentary's omission to reveal that the narrator's male guardian served in a post in the Hamas-controlled authority was materially misleading.
"Consequently that the public did not have essential details which may have been highly relevant to their evaluation of the voice and the information he shared.
"Credibility is at the core of the connection between a media organization and its viewers, especially for a public service broadcaster such as the BBC.
"This oversight had the risk to erode the significantly high levels of credibility that audiences would have put in a BBC factual programme about the Gaza conflict."
The programme was removed from the BBC's streaming service in the month of February after the presenter's family links emerged, and in July an internal BBC review found it violated the organization's editorial guidelines on factual correctness.
A BBC spokesperson said: "The authority's determination is in line with the findings of the internal assessment, that there was a major oversight in the film in relation to the corporation's content standards on factual correctness, which aligns with Rule 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we accept the authority's determination in complete. We will follow the directive as soon as the timing and language are confirmed."
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