The public service broadcaster was found to have committed a "significant breach" of broadcasting rules by omitting to mention that the narrator of a documentary about the Gaza situation was the son of a Hamas representative, according to British broadcasting authority Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the programme was "substantially inaccurate".
The head of the BBC had earlier expressed regret, saying there had been "a major oversight in relation to truthfulness".
The authority has instructed the corporation to air a peak-time statement about its decisions.
"Since this amounts to a major infringement of our regulations, we are instructing the broadcaster to broadcast a statement of our conclusions against it on BBC2 at nine o'clock in the evening, with a timing to be finalised," the regulator stated.
'Possibility to Undermine Credibility'
The watchdog's statement stated: "The inquiry we conducted found that the programme's omission to reveal that the voice's parent served in a post in the Hamas-administered authority was materially misleading.
"It meant that the public did not have critical information which may have been highly relevant to their evaluation of the narrator and the information he provided.
"Credibility is at the core of the bond between a television network and its public, notably for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the possibility to damage the exceptionally strong levels of trust that the public would have placed in a factual film from the broadcaster about the Gaza conflict."
The programme was removed from the BBC's streaming service in February after the presenter's family links came to light, and in July an corporation's own inquiry concluded it violated the corporation's editorial guidelines on truthfulness.
A corporation official stated: "The authority's determination is in accordance with the findings of the internal assessment, that there was a serious error in the film in relation to the broadcaster's journalistic policies on factual correctness, which reflects clause 2.2 of the regulator's media standards.
"We have apologised for this and we accept the regulator's ruling in its entirety. We will comply with the penalty as soon as the schedule and language are finalised."
