The public service broadcaster was found to have committed a "major breach" of industry standards by failing to disclose that the voice of a programme about the Gaza conflict was the offspring of a Hamas official, as determined by regulatory body Ofcom.
An probe by Ofcom into the programme Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The head of the BBC had earlier expressed regret, noting there had been "a significant failing in relation to truthfulness".
The regulator has directed the broadcaster to broadcast a peak-time statement about its conclusions.
"As this represents a major infringement of our regulations, we are instructing the corporation to air a statement of our findings against it on the BBC's second channel at 9pm, with a timing to be confirmed," it said.
'Possibility to Undermine Trust'
The authority's announcement stated: "The inquiry we conducted found that the programme's lack of disclosure that the voice's parent occupied a role in the Hamas-run authority was significantly deceptive.
"It meant that the public did not have vital facts which may have been highly relevant to their judgment of the voice and the content he provided.
"Confidence is at the heart of the relationship between a broadcaster and its public, especially for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the potential to erode the exceptionally strong degrees of confidence that viewers would have placed in a documentary produced by the BBC about the Gaza conflict."
The programme was pulled from the BBC's streaming service in the month of February after the presenter's familial connections came to light, and in the month of July an broadcaster's internal assessment determined it breached the organization's journalistic standards on accuracy.
A BBC spokesperson said: "The regulator's decision is in agreement with the results of the internal assessment, that there was a serious error in the film in relation to the corporation's content standards on truthfulness, which aligns with regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with the regulator's ruling in its entirety. We will follow the penalty as soon as the schedule and wording are confirmed."
