The public service broadcaster was found to have committed a "serious breach" of media regulations by not revealing that the voice of a documentary about the Gaza situation was the offspring of a Hamas official, as ruled by UK media regulator Ofcom.
An inquiry by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The chief executive of the broadcaster had already issued an apology, stating there had been "a serious error in relation to truthfulness".
The regulator has directed the BBC to broadcast a evening statement about its decisions.
"As this represents a major infringement of our code, we are directing the broadcaster to air a statement of our determinations against it on the BBC's second channel at 9pm, with a timing to be determined," the statement read.
The authority's announcement said: "Our probe determined that the programme's failure to disclose that the narrator's father occupied a post in the Hamas-run administration was substantially inaccurate.
"It meant that the public did not have vital facts which may have been extremely pertinent to their judgment of the narrator and the content he provided.
"Credibility is at the core of the connection between a broadcaster and its audience, notably for a national broadcasting corporation such as the public broadcaster.
"This failing had the possibility to erode the very considerable amounts of confidence that the public would have invested in a BBC factual programme about the conflict in Gaza."
The programme was removed from the BBC's streaming service in last February after the presenter's family links emerged, and in July an internal BBC review determined it infringed the organization's content policies on accuracy.
A representative for the broadcaster said: "The Ofcom ruling is in accordance with the findings of the internal assessment, that there was a significant failing in the programme in relation to the corporation's content standards on accuracy, which corresponds to clause 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we agree with the authority's determination in its entirety. We will follow the directive as soon as the timing and language are determined."