The public service broadcaster was found to have committed a "significant breach" of industry standards by not revealing that the voice of a documentary about the Gaza situation was the offspring of a Hamas administrator, as determined by regulatory body Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has found that the programme was "materially misleading".
The BBC's director general had already issued an apology, saying there had been "a serious error in relation to accuracy".
The authority has ordered the BBC to broadcast a prime-time announcement about its decisions.
"Since this amounts to a major infringement of our code, we are instructing the broadcaster to air a statement of our findings against it on the BBC's second channel at 21:00, with a timing to be finalised," the statement read.
'Potential to Erode Credibility'
The authority's statement declared: "The inquiry we conducted determined that the programme's omission to reveal that the narrator's father served in a position in the Hamas-administered authority was materially misleading.
"Consequently that the viewers did not have critical information which may have been highly relevant to their assessment of the voice and the information he presented.
"Credibility is at the core of the relationship between a broadcaster and its public, notably for a public service broadcaster such as the British Broadcasting Corporation.
"This oversight had the potential to damage the very considerable amounts of credibility that audiences would have placed in a factual film from the broadcaster about the conflict in Gaza."
The documentary was withdrawn from iPlayer in last February after the presenter's familial connections came to light, and in July an broadcaster's internal assessment concluded it breached the corporation's content policies on factual correctness.
A corporation official stated: "The authority's determination is in agreement with the results of the internal assessment, that there was a serious error in the documentary in relation to the broadcaster's journalistic policies on accuracy, which aligns with Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we comply with Ofcom's decision in full. We will adhere to the penalty as soon as the schedule and language are finalised."
