The public service broadcaster engaged in a "serious breach" of broadcasting rules by failing to disclose that the voice of a programme about the Gaza conflict was the offspring of a Hamas representative, as determined by regulatory body Ofcom.
An inquiry by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the documentary was "significantly deceptive".
The BBC's director general had already issued an apology, saying there had been "a serious error in relation to accuracy".
The regulator has directed the corporation to broadcast a peak-time announcement about its findings.
"Since this amounts to a serious breach of our regulations, we are directing the BBC to air a announcement of our conclusions against it on the BBC's second channel at 9pm, with a timing to be determined," it said.
'Possibility to Erode Credibility'
The regulator's report stated: "Our probe found that the film's failure to disclose that the voice's parent occupied a position in the Hamas-controlled government was materially misleading.
"This implied that the audience did not have critical information which may have been highly relevant to their judgment of the narrator and the content he shared.
"Credibility is at the heart of the bond between a broadcaster and its public, especially for a public service broadcaster such as the public broadcaster.
"This error had the risk to erode the significantly high amounts of confidence that the public would have put in a documentary produced by the BBC about the Gaza conflict."
The programme was withdrawn from the BBC's streaming service in last February after the narrator's family links were revealed, and in the month of July an broadcaster's internal assessment concluded it violated the corporation's editorial guidelines on factual correctness.
A representative for the broadcaster stated: "The Ofcom ruling is in line with the findings of the internal assessment, that there was a significant failing in the documentary in relation to the BBC's Editorial Guidelines on accuracy, which reflects Rule 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we agree with Ofcom's decision in complete. We will comply with the penalty as soon as the date and language are confirmed."
