The public service broadcaster committed a "significant breach" of industry standards by omitting to mention that the presenter of a programme about Gaza was the offspring of a Hamas representative, as determined by British broadcasting authority Ofcom.
An probe by the media regulator into the documentary titled Gaza: How to Survive a Warzone has concluded that the documentary was "substantially inaccurate".
The BBC's director general had already issued an apology, stating there had been "a significant failing in relation to accuracy".
The authority has ordered the BBC to transmit a evening announcement about its decisions.
"Given this constitutes a major infringement of our rules, we are instructing the broadcaster to transmit a message of our findings against it on BBC2 at 21:00, with a schedule to be confirmed," the regulator stated.
'Potential to Erode Trust'
The regulator's announcement stated: "Our probe determined that the programme's lack of disclosure that the presenter's parent occupied a role in the Hamas-controlled administration was materially misleading.
"Consequently that the audience did not have vital facts which may have been highly relevant to their assessment of the narrator and the details he provided.
"Confidence is at the center of the relationship between a media organization and its public, notably for a national broadcasting corporation such as the public broadcaster.
"This error had the possibility to undermine the significantly high degrees of credibility that the public would have invested in a BBC factual programme about the Israel-Gaza war."
The film was removed from the BBC's streaming service in February after the presenter's personal associations emerged, and in July an internal BBC review determined it breached the corporation's editorial guidelines on truthfulness.
A BBC spokesperson said: "The Ofcom ruling is in line with the results of the corporation's inquiry, that there was a serious error in the film in relation to the corporation's content standards on accuracy, which aligns with regulation 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we agree with the regulator's ruling in its entirety. We will comply with the penalty as soon as the date and language are confirmed."