The public service broadcaster committed a "serious breach" of industry standards by omitting to mention that the voice of a documentary about the Gaza conflict was the offspring of a Hamas administrator, as ruled by British broadcasting authority Ofcom.
An inquiry by Ofcom into Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The head of the BBC had earlier expressed regret, stating there had been "a major oversight in relation to accuracy".
The regulator has directed the BBC to air a evening announcement about its decisions.
"Given this constitutes a major infringement of our rules, we are ordering the BBC to transmit a statement of our findings against it on the BBC's second channel at 9pm, with a schedule to be confirmed," the regulator stated.
'Risk to Erode Confidence'
The authority's report declared: "The inquiry we conducted concluded that the documentary's omission to reveal that the narrator's male guardian served in a post in the Hamas-controlled administration was substantially inaccurate.
"Consequently that the audience did not have essential details which may have been highly relevant to their evaluation of the voice and the content he presented.
"Trust is at the heart of the connection between a broadcaster and its viewers, particularly for a state-funded media outlet such as the BBC.
"This oversight had the potential to erode the exceptionally strong degrees of trust that viewers would have placed in a BBC factual programme about the conflict in Gaza."
The film was withdrawn from iPlayer in February after the presenter's family links came to light, and in the month of July an internal BBC review determined it breached the corporation's journalistic standards on truthfulness.
A corporation official said: "The authority's determination is in accordance with the results of Peter Johnston's review, that there was a significant failing in the film in relation to the corporation's content standards on factual correctness, which corresponds to regulation 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we agree with the regulator's ruling in complete. We will follow the sanction as soon as the date and wording are finalised."
