The public service broadcaster engaged in a "serious breach" of media regulations by omitting to mention that the voice of a film about Gaza was the offspring of a Hamas official, as determined by British broadcasting authority Ofcom.
An probe by the media regulator into the documentary titled Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The BBC's director general had previously apologised, stating there had been "a serious error in relation to accuracy".
The authority has ordered the BBC to broadcast a prime-time declaration about its conclusions.
"As this represents a significant violation of our code, we are ordering the corporation to broadcast a statement of our conclusions against it on the BBC's second channel at nine o'clock in the evening, with a timing to be determined," it said.
'Possibility to Damage Confidence'
The regulator's announcement said: "The inquiry we conducted concluded that the film's lack of disclosure that the narrator's parent held a position in the Hamas-run administration was substantially inaccurate.
"Consequently that the viewers did not have critical information which may have been extremely pertinent to their assessment of the voice and the content he provided.
"Trust is at the core of the connection between a broadcaster and its public, notably for a public service broadcaster such as the public broadcaster.
"This error had the possibility to damage the significantly high amounts of credibility that audiences would have invested in a documentary produced by the BBC about the conflict in Gaza."
The film was removed from the BBC's streaming service in last February after the boy's familial connections came to light, and in July an internal BBC review concluded it breached the organization's editorial guidelines on factual correctness.
A corporation official commented: "The Ofcom ruling is in accordance with the results of Peter Johnston's review, that there was a serious error in the film in relation to the corporation's content standards on truthfulness, which reflects Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we accept the regulator's ruling in full. We will adhere to the penalty as soon as the date and wording are determined."
