The British broadcaster committed a "major breach" of media regulations by omitting to mention that the narrator of a programme about the Gaza situation was the son of a Hamas representative, as ruled by British broadcasting authority Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the film was "significantly deceptive".
The BBC's director general had earlier expressed regret, saying there had been "a major oversight in relation to accuracy".
The authority has ordered the BBC to broadcast a prime-time statement about its findings.
"Since this amounts to a serious breach of our regulations, we are instructing the broadcaster to broadcast a announcement of our determinations against it on BBC2 at 9pm, with a date to be confirmed," the statement read.
'Potential to Undermine Trust'
The authority's statement declared: "Our probe determined that the documentary's omission to reveal that the presenter's parent held a post in the Hamas-controlled authority was materially misleading.
"This implied that the public did not have critical information which may have been highly relevant to their judgment of the presenter and the information he shared.
"Credibility is at the core of the bond between a television network and its viewers, especially for a state-funded media outlet such as the British Broadcasting Corporation.
"This oversight had the risk to erode the significantly high degrees of credibility that the public would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The programme was removed from the online platform in the month of February after the boy's family links were revealed, and in July an broadcaster's internal assessment determined it infringed the corporation's journalistic standards on accuracy.
A BBC spokesperson said: "The regulator's decision is in accordance with the results of the corporation's inquiry, that there was a serious error in the programme in relation to the corporation's content standards on accuracy, which aligns with Rule 2.2 of the regulator's media standards.
"We expressed regret for this and we comply with the authority's determination in full. We will adhere to the penalty as soon as the schedule and wording are finalised."