The public service broadcaster was found to have committed a "serious breach" of industry standards by not revealing that the presenter of a documentary about Gaza was the son of a Hamas representative, as determined by British broadcasting authority Ofcom.
An inquiry by the media regulator into the documentary titled Gaza: How to Survive a Warzone has concluded that the programme was "substantially inaccurate".
The BBC's director general had already issued an apology, saying there had been "a serious error in relation to accuracy".
The authority has ordered the broadcaster to broadcast a peak-time announcement about its decisions.
"As this represents a significant violation of our regulations, we are ordering the corporation to transmit a statement of our conclusions against it on BBC Two at 21:00, with a schedule to be finalised," it said.
'Potential to Erode Trust'
The authority's announcement stated: "Our probe determined that the documentary's omission to reveal that the presenter's parent occupied a post in the Hamas-administered administration was significantly deceptive.
"Consequently that the audience did not have critical information which may have been very significant to their judgment of the presenter and the details he provided.
"Credibility is at the core of the connection between a media organization and its public, notably for a state-funded media outlet such as the public broadcaster.
"This error had the risk to damage the very considerable degrees of confidence that viewers would have placed in a BBC factual programme about the Israel-Gaza war."
The film was removed from the BBC's streaming service in last February after the boy's family links came to light, and in July an corporation's own inquiry determined it infringed the organization's editorial guidelines on truthfulness.
A BBC spokesperson said: "The authority's determination is in line with the findings of the corporation's inquiry, that there was a serious error in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which reflects clause 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we accept Ofcom's decision in complete. We will follow the penalty as soon as the schedule and wording are finalised."
