The British broadcaster committed a "significant breach" of media regulations by not revealing that the voice of a documentary about the Gaza situation was the child of a Hamas administrator, as ruled by regulatory body Ofcom.
An probe by Ofcom into Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The chief executive of the broadcaster had already issued an apology, stating there had been "a serious error in relation to truthfulness".
The authority has instructed the corporation to broadcast a peak-time announcement about its conclusions.
"Given this constitutes a significant violation of our rules, we are instructing the broadcaster to transmit a announcement of our findings against it on BBC2 at nine o'clock in the evening, with a date to be finalised," the regulator stated.
'Possibility to Erode Confidence'
The watchdog's report declared: "The inquiry we conducted concluded that the film's lack of disclosure that the narrator's father served in a post in the Hamas-controlled government was significantly deceptive.
"Consequently that the audience did not have critical information which may have been highly relevant to their judgment of the presenter and the details he shared.
"Trust is at the core of the connection between a television network and its audience, notably for a state-funded media outlet such as the public broadcaster.
"This error had the risk to damage the exceptionally strong degrees of trust 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 last February after the presenter's familial connections emerged, and in July an corporation's own inquiry concluded it violated the organization's journalistic standards on truthfulness.
A corporation official said: "The regulator's decision is in accordance with the findings of Peter Johnston's review, that there was a significant failing in the programme in relation to the broadcaster's journalistic policies on factual correctness, which aligns with Rule 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we comply with Ofcom's decision in full. We will adhere to the penalty as soon as the date and language are determined."