The British broadcaster engaged in a "major breach" of industry standards by omitting to mention that the voice of a programme about the Gaza situation was the child of a Hamas administrator, as determined by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the film was "substantially inaccurate".
The BBC's director general had already issued an apology, noting there had been "a serious error in relation to truthfulness".
The regulator has ordered the corporation to transmit a prime-time statement about its decisions.
"Given this constitutes a major infringement of our rules, we are ordering the broadcaster to air a announcement of our findings against it on the BBC's second channel at 9pm, with a date to be finalised," it said.
'Possibility to Damage Trust'
The regulator's statement said: "Our investigation concluded that the film's lack of disclosure that the voice's father held a position in the Hamas-administered administration was materially misleading.
"This implied that the audience did not have vital facts which may have been very significant to their judgment of the narrator and the content he shared.
"Trust is at the heart of the relationship between a media organization and its viewers, especially for a national broadcasting corporation such as the BBC.
"This failing had the potential to damage the very considerable levels of credibility that the public would have put in a factual film from the broadcaster about the Gaza conflict."
The programme was withdrawn from the BBC's streaming service in the month of February after the narrator's familial connections emerged, and in this past July an internal BBC review found it violated the broadcaster's journalistic standards on factual correctness.
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 programme in relation to the corporation's content standards on factual correctness, which aligns with Rule 2.2 of the regulator's media standards.
"We have apologised for this and we comply with the authority's determination in full. We will comply with the penalty as soon as the date and wording are confirmed."