The public service broadcaster engaged in a "significant breach" of broadcasting rules by omitting to mention that the presenter of a documentary about Gaza was the son of a Hamas administrator, as determined by UK media regulator Ofcom.
An probe by Ofcom into Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The chief executive of the broadcaster had previously apologised, noting there had been "a major oversight in relation to factual correctness".
The authority has ordered the corporation to broadcast a peak-time declaration about its decisions.
"As this represents a major infringement of our rules, we are instructing the BBC to transmit a message of our conclusions against it on BBC Two at 9pm, with a schedule to be finalised," it said.
'Potential to Damage Trust'
The authority's report declared: "Our probe concluded that the programme's omission to reveal that the voice's father occupied a position in the Hamas-controlled government was substantially inaccurate.
"It meant that the audience did not have critical information which may have been highly relevant to their judgment of the voice and the content he provided.
"Trust is at the core of the connection between a television network and its public, notably for a public service broadcaster such as the British Broadcasting Corporation.
"This oversight had the risk to undermine the very considerable degrees of trust that viewers would have invested in a documentary produced by the BBC about the Gaza conflict."
The programme was withdrawn from iPlayer in February after the boy's familial connections were revealed, and in this past July an corporation's own inquiry determined it violated the broadcaster's editorial guidelines on truthfulness.
A representative for the broadcaster said: "The Ofcom ruling is in agreement with the findings of the corporation's inquiry, that there was a serious error in the programme in relation to the broadcaster's journalistic policies on factual correctness, which corresponds to regulation 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with the authority's determination in complete. We will comply with the penalty as soon as the date and wording are determined."
