The British broadcaster committed a "major breach" of media regulations by omitting to mention that the narrator of a programme about the Gaza conflict was the child of a Hamas official, as determined by UK media regulator Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The BBC's director general had earlier expressed regret, stating there had been "a serious error in relation to truthfulness".
The authority has ordered the BBC to transmit a evening statement about its conclusions.
"Given this constitutes a significant violation of our regulations, we are directing the BBC to air a statement of our conclusions against it on BBC Two at 21:00, with a timing to be determined," it said.
'Possibility to Erode Trust'
The watchdog's report stated: "The inquiry we conducted concluded that the programme's omission to reveal that the voice's father held a post in the Hamas-administered government was materially misleading.
"It meant that the public did not have vital facts which may have been very significant to their judgment of the presenter and the details he presented.
"Confidence is at the center of the connection between a television network and its viewers, notably for a national broadcasting corporation such as the BBC.
"This oversight had the possibility to damage the significantly high degrees of trust that viewers would have put in a factual film from the broadcaster about the conflict in Gaza."
The programme was pulled from the BBC's streaming service in the month of February after the boy's familial connections emerged, and in the month of July an internal BBC review concluded it breached the corporation's editorial guidelines on accuracy.
A BBC spokesperson stated: "The regulator's decision is in agreement with the findings of Peter Johnston's review, that there was a serious error in the film in relation to the broadcaster's journalistic policies on accuracy, which reflects regulation 2.2 of the regulator's media standards.
"We issued an apology for this and we comply with the regulator's ruling in full. We will follow the penalty as soon as the date and wording are finalised."