The public service broadcaster was found to have committed a "major breach" of industry standards by failing to disclose that the narrator of a documentary about the Gaza conflict was the son of a Hamas administrator, as ruled by regulatory body Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has concluded that the documentary was "significantly deceptive".
The BBC's director general had already issued an apology, noting there had been "a significant failing in relation to factual correctness".
The regulator has ordered the broadcaster to transmit a evening announcement about its conclusions.
"Since this amounts to a significant violation of our code, we are directing the broadcaster to broadcast a announcement of our determinations against it on the BBC's second channel at nine o'clock in the evening, with a timing to be confirmed," the regulator stated.
'Risk to Damage Confidence'
The authority's statement stated: "Our investigation determined that the documentary's lack of disclosure that the voice's father held a post in the Hamas-controlled administration was materially misleading.
"It meant that the public did not have essential details which may have been highly relevant to their assessment of the presenter and the content he shared.
"Credibility is at the heart of the connection between a broadcaster and its public, notably for a public service broadcaster such as the BBC.
"This failing had the possibility to erode the very considerable levels of trust that audiences would have invested in a documentary produced by the BBC about the conflict in Gaza."
The programme was removed from the BBC's streaming service in February after the boy's personal associations emerged, and in this past July an internal BBC review found it breached the corporation's editorial guidelines on truthfulness.
A BBC spokesperson said: "The authority's determination is in accordance with the results of the internal assessment, that there was a serious error in the film in relation to the BBC's Editorial Guidelines on accuracy, which corresponds to regulation 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we comply with the regulator's ruling in complete. We will adhere to the penalty as soon as the schedule and wording are finalised."