The public service broadcaster was found to have committed a "serious breach" of broadcasting rules by not revealing that the presenter of a documentary about Gaza was the child of a Hamas official, as ruled by regulatory body Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The BBC's director general had earlier expressed regret, noting there had been "a significant failing in relation to factual correctness".
The regulator has instructed the broadcaster to broadcast a peak-time statement about its decisions.
"As this represents a serious breach of our code, we are ordering the broadcaster to transmit a announcement of our determinations against it on BBC2 at 21:00, with a timing to be confirmed," it said.
'Possibility to Damage Trust'
The authority's report stated: "Our probe determined that the programme's failure to disclose that the voice's parent occupied a role in the Hamas-run authority was materially misleading.
"It meant that the audience did not have vital facts which may have been highly relevant to their evaluation of the narrator and the information he provided.
"Credibility is at the core of the relationship between a television network and its audience, especially for a public service broadcaster such as the British Broadcasting Corporation.
"This error had the possibility to undermine the significantly high degrees of trust that audiences would have invested in a BBC factual programme about the Israel-Gaza war."
The film was withdrawn from iPlayer in last February after the narrator's personal associations emerged, and in this past July an broadcaster's internal assessment determined it violated the organization's journalistic standards on factual correctness.
A BBC spokesperson said: "The regulator's decision is in accordance with the conclusions of the corporation's inquiry, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on factual correctness, which aligns with clause 2.2 of the regulator's media standards.
"We issued an apology for this and we accept the authority's determination in full. We will comply with the penalty as soon as the schedule and wording are determined."
