The public service broadcaster engaged in a "major breach" of broadcasting rules by not revealing that the voice of a documentary about the Gaza situation was the offspring of a Hamas official, as ruled by UK media regulator Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the film was "materially misleading".
The BBC's director general had already issued an apology, noting there had been "a serious error in relation to accuracy".
Ofcom has ordered the corporation to broadcast a prime-time declaration about its conclusions.
"Since this amounts to a serious breach of our rules, we are ordering the BBC to air a announcement of our conclusions against it on BBC2 at 9pm, with a schedule to be finalised," it said.
'Potential to Erode Credibility'
The authority's statement stated: "The inquiry we conducted found that the documentary's failure to disclose that the voice's parent occupied a role in the Hamas-run government was materially misleading.
"It meant that the viewers did not have essential details which may have been extremely pertinent to their evaluation of the narrator and the content he provided.
"Confidence is at the core of the bond between a media organization and its public, particularly for a national broadcasting corporation such as the BBC.
"This error had the potential to undermine the very considerable degrees of confidence that the public would have invested in a BBC factual programme about the conflict in Gaza."
The programme was pulled from iPlayer in last February after the narrator's personal associations emerged, and in July an internal BBC review found it violated the corporation's journalistic standards on factual correctness.
A corporation official commented: "The authority's determination is in line with the findings of the internal assessment, that there was a serious error in the programme in relation to the broadcaster's journalistic policies on truthfulness, which aligns with regulation 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we comply with Ofcom's decision in its entirety. We will comply with the penalty as soon as the schedule and language are determined."
