The public service broadcaster was found to have committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a documentary about the Gaza conflict was the offspring of a Hamas representative, as determined by British broadcasting authority Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the documentary was "materially misleading".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a serious error in relation to factual correctness".
Ofcom has instructed the broadcaster to broadcast a evening announcement about its decisions.
"As this represents a major infringement of our code, we are instructing the broadcaster to air a message of our determinations against it on the BBC's second channel at nine o'clock in the evening, with a schedule to be finalised," it said.
'Potential to Erode Credibility'
The regulator's announcement said: "Our probe concluded that the film's lack of disclosure that the narrator's male guardian held a position in the Hamas-administered government was materially misleading.
"Consequently that the audience did not have critical information which may have been highly relevant to their evaluation of the presenter and the content he shared.
"Confidence is at the core of the bond between a media organization and its audience, notably for a public service broadcaster such as the BBC.
"This failing had the possibility to damage the exceptionally strong degrees of confidence that viewers would have put in a documentary produced by the BBC about the Gaza conflict."
The film was withdrawn from the online platform in February after the narrator's personal associations were revealed, and in July an corporation's own inquiry found it breached the corporation's journalistic standards on accuracy.
A representative for the broadcaster stated: "The Ofcom ruling is in line with the findings of the internal assessment, that there was a major oversight in the programme in relation to the BBC's Editorial Guidelines on factual correctness, which aligns with Rule 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we comply with Ofcom's decision in complete. We will adhere to the penalty as soon as the schedule and wording are determined."