The British broadcaster committed a "major breach" of industry standards by omitting to mention that the narrator of a documentary about Gaza was the child of a Hamas administrator, as determined by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the programme was "materially misleading".
The head of the BBC had already issued an apology, saying there had been "a major oversight in relation to accuracy".
Ofcom has ordered the corporation to transmit a evening announcement about its findings.
"As this represents a major infringement of our rules, we are ordering the corporation to broadcast a announcement of our conclusions against it on BBC Two at nine o'clock in the evening, with a date to be finalised," it said.
'Risk to Damage Trust'
The authority's announcement said: "Our probe found that the programme's omission to reveal that the voice's male guardian held a post in the Hamas-controlled authority was materially misleading.
"This implied that the viewers did not have critical information which may have been extremely pertinent to their judgment of the narrator and the information he presented.
"Confidence is at the heart of the connection between a media organization and its viewers, particularly for a national broadcasting corporation such as the BBC.
"This error had the possibility to damage the very considerable degrees of credibility that audiences would have invested in a documentary produced by the BBC about the conflict in Gaza."
The programme was removed from the BBC's streaming service in February after the boy's familial connections were revealed, and in this past July an corporation's own inquiry concluded it breached the organization's journalistic standards on factual correctness.
A BBC spokesperson stated: "The Ofcom ruling is in agreement with the results of the internal assessment, that there was a serious error in the programme in relation to the corporation's content standards on accuracy, which corresponds to regulation 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we comply with Ofcom's decision in complete. We will follow the penalty as soon as the schedule and wording are confirmed."