The public service broadcaster was found to have committed a "major breach" of industry standards by omitting to mention that the voice of a film about the Gaza situation was the son of a Hamas official, as determined by UK media regulator Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The BBC's director general had already issued an apology, noting there had been "a serious error in relation to factual correctness".
Ofcom has directed the broadcaster to air a evening announcement about its conclusions.
"Given this constitutes a major infringement of our rules, we are ordering the BBC to air a statement of our findings against it on the BBC's second channel at 9pm, with a date to be confirmed," it said.
'Risk to Damage Confidence'
The regulator's announcement declared: "Our investigation concluded that the documentary's lack of disclosure that the narrator's parent held a position in the Hamas-controlled administration was materially misleading.
"Consequently that the viewers did not have vital facts which may have been very significant to their evaluation of the voice and the content he provided.
"Credibility is at the core of the bond between a media organization and its viewers, particularly for a national broadcasting corporation such as the public broadcaster.
"This error had the risk to undermine the very considerable amounts of confidence that the public would have invested in a BBC factual programme about the Israel-Gaza war."
The film was pulled from the online platform in February after the presenter's family links were revealed, and in July an corporation's own inquiry determined it infringed the organization's content policies on accuracy.
A corporation official stated: "The Ofcom ruling is in line with the findings of the internal assessment, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on accuracy, which corresponds to regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with the authority's determination in its entirety. We will comply with the penalty as soon as the schedule and wording are confirmed."
