The British broadcaster was found to have committed a "major breach" of industry standards by failing to disclose that the voice of a documentary about the Gaza conflict was the child of a Hamas official, as determined by UK media regulator Ofcom.
An investigation by Ofcom into Gaza: How to Survive a Warzone has determined that the film was "materially misleading".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a major oversight in relation to truthfulness".
The regulator has ordered the broadcaster to air a peak-time statement about its findings.
"Since this amounts to a major infringement of our code, we are ordering the broadcaster to broadcast a announcement of our conclusions against it on BBC Two at 9pm, with a schedule to be confirmed," it said.
'Potential to Damage Confidence'
The regulator's announcement said: "Our investigation determined that the documentary's failure to disclose that the presenter's parent held a role in the Hamas-administered authority was materially misleading.
"It meant that the public did not have critical information which may have been very significant to their judgment of the presenter and the details he shared.
"Credibility is at the core of the relationship between a media organization and its audience, particularly for a national broadcasting corporation such as the public broadcaster.
"This oversight had the potential to undermine the exceptionally strong levels of credibility that the public would have put in a documentary produced by the BBC about the Gaza conflict."
The film was pulled from the online platform in last February after the presenter's family links emerged, and in this past July an broadcaster's internal assessment determined it violated the broadcaster's content policies on factual correctness.
A corporation official stated: "The authority's determination is in agreement with the conclusions of Peter Johnston's review, that there was a significant failing in the programme in relation to the corporation's content standards on factual correctness, which aligns with clause 2.2 of the regulator's media standards.
"We expressed regret for this and we accept Ofcom's decision in complete. We will comply with the penalty as soon as the date and wording are confirmed."
