The public service broadcaster engaged in a "serious breach" of industry standards by omitting to mention that the voice of a film about Gaza was the son of a Hamas administrator, as ruled by UK media regulator Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The BBC's director general had previously apologised, saying there had been "a serious error in relation to factual correctness".
Ofcom has directed the BBC to air a peak-time declaration about its findings.
"Since this amounts to a major infringement of our rules, we are ordering the BBC to broadcast a statement of our conclusions against it on the BBC's second channel at 21:00, with a date to be finalised," the statement read.
'Risk to Erode Credibility'
The watchdog's report declared: "The inquiry we conducted determined that the documentary's omission to reveal that the voice's male guardian occupied a position in the Hamas-controlled authority was materially misleading.
"This implied that the audience did not have essential details which may have been extremely pertinent to their judgment of the narrator and the content he provided.
"Confidence is at the center of the relationship between a broadcaster and its viewers, especially for a national broadcasting corporation such as the British Broadcasting Corporation.
"This failing had the risk to undermine the significantly high degrees of confidence that the public would have put in a documentary produced by the BBC about the Gaza conflict."
The film was pulled from the BBC's streaming service in last February after the presenter's family links were revealed, and in this past July an broadcaster's internal assessment determined it breached the organization's journalistic standards on truthfulness.
A representative for the broadcaster said: "The Ofcom ruling is in accordance with the results of Peter Johnston's review, that there was a significant failing in the film in relation to the BBC's Editorial Guidelines on truthfulness, which reflects Rule 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we agree with the authority's determination in full. We will follow the penalty as soon as the schedule and wording are finalised."
