The public service broadcaster engaged in a "major breach" of industry standards by not revealing that the presenter of a programme about Gaza was the offspring of a Hamas representative, as ruled by regulatory body Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has found that the documentary was "substantially inaccurate".
The BBC's director general had previously apologised, stating there had been "a significant failing in relation to accuracy".
The authority has ordered the BBC to transmit a peak-time declaration about its conclusions.
"As this represents a significant violation of our rules, we are instructing the corporation to broadcast a announcement of our determinations against it on BBC2 at 9pm, with a timing to be confirmed," the statement read.
'Possibility to Damage Credibility'
The authority's announcement said: "Our investigation found that the programme's failure to disclose that the voice's parent occupied a post in the Hamas-administered government was significantly deceptive.
"Consequently that the viewers did not have essential details which may have been extremely pertinent to their assessment of the voice and the information he shared.
"Credibility is at the heart of the relationship between a media organization and its viewers, especially for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the possibility to damage the very considerable amounts of trust that viewers would have put in a factual film from the broadcaster about the Israel-Gaza war."
The programme was removed from iPlayer in last February after the narrator's personal associations came to light, and in July an broadcaster's internal assessment found it breached the corporation's journalistic standards on accuracy.
A BBC spokesperson said: "The regulator's decision is in line with the results of Peter Johnston's review, that there was a major oversight in the film in relation to the BBC's Editorial Guidelines on accuracy, which corresponds to Rule 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we accept the authority's determination in full. We will comply with the penalty as soon as the schedule and language are confirmed."
