The public service broadcaster was found to have committed a "significant breach" of industry standards by omitting to mention that the voice of a programme about the Gaza situation was the offspring of a Hamas administrator, as ruled by regulatory body Ofcom.
An investigation by Ofcom into Gaza: How to Survive a Warzone has found that the programme was "significantly deceptive".
The BBC's director general had previously apologised, noting there had been "a serious error in relation to truthfulness".
Ofcom has instructed the corporation to broadcast a evening announcement about its findings.
"Since this amounts to a major infringement of our code, we are directing the broadcaster 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 finalised," the regulator stated.
'Possibility to Erode Confidence'
The watchdog's announcement stated: "The inquiry we conducted concluded that the film's lack of disclosure that the presenter's parent held a position in the Hamas-administered government was significantly deceptive.
"It meant that the audience did not have vital facts which may have been highly relevant to their assessment of the presenter and the details he presented.
"Trust is at the heart of the connection between a media organization and its viewers, notably for a public service broadcaster such as the British Broadcasting Corporation.
"This error had the possibility to erode the very considerable levels of confidence that viewers would have invested in a factual film from the broadcaster about the Gaza conflict."
The documentary was removed from the online platform in last February after the narrator's family links emerged, and in July an internal BBC review found it infringed the broadcaster's content policies on accuracy.
A BBC spokesperson commented: "The regulator's decision is in line with the findings of Peter Johnston's review, that there was a major oversight in the documentary in relation to the corporation's content standards on factual correctness, which corresponds to clause 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with the authority's determination in full. We will adhere to the penalty as soon as the timing and language are determined."
