The public service broadcaster was found to have committed a "serious breach" of broadcasting rules by omitting to mention that the voice of a film about Gaza was the child of a Hamas official, as ruled by UK media regulator Ofcom.
An inquiry by Ofcom into Gaza: How to Survive a Warzone has determined that the documentary was "substantially inaccurate".
The BBC's director general had already issued an apology, noting there had been "a major oversight in relation to accuracy".
The regulator has instructed the corporation to transmit a peak-time announcement about its conclusions.
"Since this amounts to a serious breach of our rules, we are ordering the broadcaster to air a announcement of our findings against it on the BBC's second channel at nine o'clock in the evening, with a schedule to be finalised," the statement read.
'Risk to Erode Credibility'
The authority's announcement stated: "Our investigation found that the programme's lack of disclosure that the presenter's male guardian held a position in the Hamas-controlled government was substantially inaccurate.
"It meant that the public did not have essential details which may have been highly relevant to their assessment of the voice and the details he shared.
"Credibility is at the heart of the bond between a television network and its audience, notably for a public service broadcaster such as the BBC.
"This error had the possibility to undermine the very considerable levels of confidence that the public would have placed in a BBC factual programme about the Gaza conflict."
The programme was pulled from iPlayer in last February after the presenter's family links emerged, and in this past July an broadcaster's internal assessment concluded it violated the organization's content policies on truthfulness.
A representative for the broadcaster said: "The regulator's decision is in accordance with the findings of the internal assessment, that there was a serious error in the film in relation to the corporation's content standards on truthfulness, which reflects clause 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with Ofcom's decision in complete. We will comply with the sanction as soon as the timing and language are confirmed."
