The public service broadcaster was found to have committed a "serious breach" of media regulations by not revealing that the voice of a film about the Gaza conflict was the offspring of a Hamas representative, as ruled by British broadcasting authority Ofcom.
An probe by the media regulator into Gaza: How to Survive a Warzone has concluded that the programme was "materially misleading".
The head of the BBC had earlier expressed regret, stating there had been "a significant failing in relation to factual correctness".
The regulator has ordered the broadcaster to transmit a peak-time statement about its findings.
"As this represents a significant violation of our rules, we are ordering the broadcaster to broadcast a message of our determinations against it on the BBC's second channel at 21:00, with a schedule to be determined," it said.
'Risk to Erode Credibility'
The watchdog's report said: "Our investigation found that the film's omission to reveal that the presenter's parent held a post in the Hamas-administered authority was materially misleading.
"This implied that the audience did not have essential details which may have been extremely pertinent to their judgment of the narrator and the information he provided.
"Credibility is at the core of the relationship between a media organization and its public, notably for a national broadcasting corporation such as the BBC.
"This oversight had the potential to damage the very considerable levels of trust that audiences would have invested in a BBC factual programme about the conflict in Gaza."
The programme was removed from the BBC's streaming service in February after the presenter's family links came to light, and in July an corporation's own inquiry determined it violated the organization's editorial guidelines on factual correctness.
A BBC spokesperson said: "The regulator's decision is in agreement with the results of Peter Johnston's review, that there was a significant failing in the programme in relation to the corporation's content standards on truthfulness, which corresponds to clause 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we comply with the regulator's ruling in complete. We will adhere to the directive as soon as the timing and language are finalised."
