The British broadcaster was found to have committed a "major breach" of broadcasting rules by failing to disclose that the voice of a documentary about Gaza was the offspring of a Hamas official, as ruled by regulatory body Ofcom.
An investigation by Ofcom into 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 major oversight in relation to accuracy".
The regulator has directed the corporation to broadcast a peak-time declaration about its findings.
"Given this constitutes a serious breach of our regulations, we are ordering the BBC to transmit a statement of our determinations against it on the BBC's second channel at 9pm, with a date to be confirmed," it said.
'Potential to Damage Confidence'
The regulator's report said: "Our investigation concluded that the programme's failure to disclose that the voice's father occupied a role in the Hamas-controlled government was substantially inaccurate.
"This implied that the viewers did not have critical information which may have been extremely pertinent to their assessment of the voice and the content he shared.
"Credibility is at the core of the bond between a media organization and its viewers, especially for a national broadcasting corporation such as the BBC.
"This error had the risk to erode the very considerable amounts of confidence that the public would have placed in a factual film from the broadcaster about the Gaza conflict."
The programme was removed from the BBC's streaming service in February after the narrator's personal associations came to light, and in the month of July an internal BBC review concluded it breached the organization's content policies on truthfulness.
A representative for the broadcaster said: "The authority's determination is in agreement with the results of Peter Johnston's review, that there was a serious error in the film in relation to the BBC's Editorial Guidelines on factual correctness, which aligns with regulation 2.2 of the regulator's media standards.
"We expressed regret for this and we accept the authority's determination in its entirety. We will adhere to the directive as soon as the schedule and language are determined."
