The public service broadcaster was found to have committed a "major breach" of industry standards by not revealing that the voice of a film about the Gaza situation was the child of a Hamas administrator, as ruled by regulatory body Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the film was "substantially inaccurate".
The BBC's director general had previously apologised, saying there had been "a significant failing in relation to truthfulness".
Ofcom has instructed the BBC to air a evening announcement about its findings.
"Since this amounts to a significant violation of our code, we are directing the BBC to broadcast a message of our determinations against it on the BBC's second channel at 21:00, with a date to be determined," it said.
'Possibility to Undermine Confidence'
The regulator's announcement stated: "Our investigation concluded that the film's failure to disclose that the presenter's male guardian occupied a post in the Hamas-administered government was substantially inaccurate.
"It meant that the audience did not have critical information which may have been very significant to their judgment of the presenter and the information he provided.
"Confidence is at the center of the connection between a television network and its audience, especially for a public service broadcaster such as the BBC.
"This failing had the potential to undermine the very considerable levels of confidence that audiences would have placed in a BBC factual programme about the Israel-Gaza war."
The documentary was pulled from the online platform in last February after the presenter's family links emerged, and in the month of July an corporation's own inquiry found it violated the organization's content policies on accuracy.
A BBC spokesperson said: "The regulator's decision is in line with the results of Peter Johnston's review, that there was a major oversight in the programme in relation to the corporation's content standards on accuracy, which reflects regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with Ofcom's decision in complete. We will follow the penalty as soon as the date and wording are finalised."
