The public service broadcaster was found to have committed a "major breach" of industry standards by omitting to mention that the voice of a film about the Gaza situation was the son of a Hamas representative, according to regulatory body Ofcom.
An probe by Ofcom into the programme Gaza: How to Survive a Warzone has found that the film was "significantly deceptive".
The chief executive of the broadcaster had already issued an apology, saying there had been "a major oversight in relation to factual correctness".
The regulator has ordered the corporation to transmit a peak-time statement about its findings.
"Since this amounts to a serious breach of our rules, we are instructing the BBC to air a message of our conclusions against it on the BBC's second channel at nine o'clock in the evening, with a schedule to be determined," it said.
'Risk to Damage Trust'
The authority's statement said: "Our investigation found that the documentary's omission to reveal that the narrator's parent held a role in the Hamas-run administration was significantly deceptive.
"Consequently that the audience did not have essential details which may have been very significant to their assessment of the voice and the content he presented.
"Confidence is at the heart of the connection between a broadcaster and its public, notably for a state-funded media outlet such as the BBC.
"This oversight had the risk to damage the exceptionally strong amounts of trust that viewers would have invested in a factual film from the broadcaster about the Gaza conflict."
The film was pulled from the BBC's streaming service in February after the presenter's familial connections emerged, and in July an corporation's own inquiry determined it breached the corporation's journalistic standards on accuracy.
A BBC spokesperson stated: "The authority's determination is in line with the findings of the corporation's inquiry, that there was a major oversight in the documentary in relation to the broadcaster's journalistic policies on accuracy, which reflects Rule 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we accept the regulator's ruling in its entirety. We will comply with the penalty as soon as the schedule and language are confirmed."
