The public service broadcaster was found to have committed a "major breach" of broadcasting rules by omitting to mention that the narrator of a programme about Gaza was the offspring of a Hamas administrator, as ruled by UK media regulator Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the documentary was "substantially inaccurate".
The head of the BBC had earlier expressed regret, saying there had been "a significant failing in relation to truthfulness".
The regulator has instructed the corporation to broadcast a prime-time announcement about its decisions.
"Given this constitutes a significant violation of our code, we are directing the corporation to broadcast a message of our conclusions against it on BBC Two at 21:00, with a timing to be confirmed," the statement read.
'Possibility to Damage Confidence'
The authority's announcement said: "Our investigation found that the documentary's failure to disclose that the presenter's male guardian held a post in the Hamas-administered administration was materially misleading.
"It meant that the public did not have vital facts which may have been highly relevant to their evaluation of the voice and the content he shared.
"Confidence is at the center of the connection between a broadcaster and its audience, especially for a public service broadcaster such as the BBC.
"This error had the risk to undermine the exceptionally strong amounts of confidence that the public would have placed in a factual film from the broadcaster about the conflict in Gaza."
The documentary was withdrawn from the online platform in last February after the presenter's family links were revealed, and in July an broadcaster's internal assessment determined it breached the corporation's editorial guidelines on factual correctness.
A BBC spokesperson said: "The regulator's decision is in line with the conclusions of Peter Johnston's review, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on accuracy, which corresponds to Rule 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we agree with the regulator's ruling in complete. We will follow the penalty as soon as the schedule and wording are determined."