The public service broadcaster was found to have committed a "serious breach" of broadcasting rules by not revealing that the voice of a programme about the Gaza situation was the child of a Hamas administrator, as determined by British broadcasting authority Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the programme was "materially misleading".
The chief executive of the broadcaster had previously apologised, saying there had been "a major oversight in relation to factual correctness".
The regulator has ordered the corporation to broadcast a prime-time statement about its findings.
"As this represents a significant violation of our rules, we are ordering the BBC to transmit a statement of our determinations against it on the BBC's second channel at 9pm, with a schedule to be confirmed," the regulator stated.
'Potential to Damage Trust'
The authority's report said: "Our investigation found that the documentary's omission to reveal that the presenter's male guardian held a role in the Hamas-administered government was substantially inaccurate.
"Consequently that the public did not have essential details which may have been highly relevant to their assessment of the narrator and the details he presented.
"Confidence is at the core of the relationship between a television network and its audience, especially for a state-funded media outlet such as the public broadcaster.
"This error had the risk to damage the significantly high amounts of credibility that the public would have placed in a BBC factual programme about the conflict in Gaza."
The programme was pulled from the online platform in February after the presenter's family links were revealed, and in this past July an corporation's own inquiry concluded it breached the corporation's editorial guidelines on truthfulness.
A representative for the broadcaster said: "The Ofcom ruling is in line with the results of Peter Johnston's review, that there was a serious error in the film in relation to the BBC's Editorial Guidelines on accuracy, which reflects regulation 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with Ofcom's decision in full. We will adhere to the penalty as soon as the date and wording are determined."
