The public service broadcaster was found to have committed a "serious breach" of industry standards by omitting to mention that the voice of a programme about the Gaza conflict was the offspring of a Hamas official, as ruled by British broadcasting authority Ofcom.
An probe by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the film was "materially misleading".
The head of the BBC had earlier expressed regret, saying there had been "a major oversight in relation to truthfulness".
The regulator has ordered the BBC to transmit a prime-time declaration about its conclusions.
"Given this constitutes a serious breach of our code, we are ordering the corporation to air a announcement of our findings against it on BBC Two at 9pm, with a schedule to be determined," it said.
'Possibility to Damage Credibility'
The watchdog's statement said: "Our investigation determined that the film's omission to reveal that the voice's father occupied a position in the Hamas-run government was materially misleading.
"It meant that the viewers did not have essential details which may have been very significant to their judgment of the voice and the content he presented.
"Credibility is at the heart of the relationship between a broadcaster and its public, particularly for a state-funded media outlet such as the public broadcaster.
"This oversight had the potential to erode the exceptionally strong levels of confidence that the public would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The documentary was removed from the online platform in February after the presenter's familial connections were revealed, and in July an internal BBC review found it infringed the corporation's journalistic standards on factual correctness.
A representative for the broadcaster commented: "The Ofcom ruling is in agreement with the findings of the internal assessment, that there was a major oversight in the documentary in relation to the corporation's content standards on accuracy, which aligns with regulation 2.2 of the regulator's media standards.
"We issued an apology for this and we agree with the regulator's ruling in full. We will comply with the penalty as soon as the schedule and language are determined."
