The public service broadcaster engaged in a "serious breach" of broadcasting rules by failing to disclose that the voice of a programme about Gaza was the child of a Hamas representative, according to regulatory body Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The chief executive of the broadcaster had previously apologised, noting there had been "a significant failing in relation to truthfulness".
The regulator has directed the BBC to broadcast a prime-time statement about its conclusions.
"Since this amounts to a serious breach of our regulations, we are ordering the corporation to transmit a announcement of our findings against it on BBC2 at 21:00, with a schedule to be finalised," it said.
'Potential to Damage Credibility'
The watchdog's statement stated: "Our probe determined that the documentary's omission to reveal that the narrator's parent served in a position in the Hamas-controlled administration was significantly deceptive.
"This implied that the viewers did not have critical information which may have been highly relevant to their assessment of the presenter and the details he presented.
"Trust is at the core of the connection between a media organization and its viewers, notably for a national broadcasting corporation such as the BBC.
"This oversight had the possibility to erode the very considerable levels of credibility that viewers would have placed in a documentary produced by the BBC about the Gaza conflict."
The documentary was pulled from the online platform in February after the narrator's familial connections emerged, and in the month of July an internal BBC review concluded it infringed the broadcaster's content policies on truthfulness.
A corporation official stated: "The regulator's decision is in accordance with the results of the internal assessment, that there was a significant failing in the programme in relation to the corporation's content standards on accuracy, which reflects regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with the authority's determination in its entirety. We will adhere to the penalty as soon as the date and language are finalised."