The public service broadcaster engaged in a "major breach" of broadcasting rules by failing to disclose that the voice of a programme about the Gaza conflict was the son of a Hamas official, as determined by regulatory body Ofcom.
An probe by the broadcasting watchdog into Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The BBC's director general had earlier expressed regret, saying there had been "a serious error in relation to accuracy".
The regulator has ordered the BBC to air a peak-time declaration about its decisions.
"Given this constitutes a serious breach of our regulations, we are instructing the broadcaster to broadcast a message of our determinations against it on BBC2 at nine o'clock in the evening, with a timing to be confirmed," it said.
'Potential to Undermine Confidence'
The watchdog's announcement declared: "Our probe determined that the programme's failure to disclose that the narrator's parent served in a position in the Hamas-controlled government was substantially inaccurate.
"Consequently that the public did not have essential details which may have been highly relevant to their evaluation of the narrator and the information he provided.
"Confidence is at the core of the bond between a television network and its public, notably for a national broadcasting corporation such as the British Broadcasting Corporation.
"This error had the potential to undermine the very considerable levels of trust that audiences would have invested in a factual film from the broadcaster about the Gaza conflict."
The programme was withdrawn from the online platform in the month of February after the boy's familial connections emerged, and in the month of July an internal BBC review found it infringed the broadcaster's editorial guidelines on accuracy.
A corporation official said: "The Ofcom ruling is in accordance with the findings of Peter Johnston's review, that there was a significant failing in the programme in relation to the broadcaster's journalistic policies on accuracy, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we agree with Ofcom's decision in complete. We will comply with the penalty as soon as the date and language are finalised."
