The public service broadcaster was found to have committed a "significant breach" of broadcasting rules by omitting to mention that the narrator of a film about the Gaza situation was the child of a Hamas administrator, as determined by regulatory body Ofcom.
An investigation by the media regulator into the programme Gaza: How to Survive a Warzone has concluded that the programme was "significantly deceptive".
The BBC's director general had earlier expressed regret, stating there had been "a significant failing in relation to accuracy".
The authority has instructed the BBC to air a prime-time statement about its decisions.
"Given this constitutes a significant violation of our rules, we are instructing the corporation to broadcast a statement of our findings against it on the BBC's second channel at 21:00, with a timing to be finalised," the statement read.
'Risk to Erode Confidence'
The watchdog's statement said: "The inquiry we conducted determined that the programme's lack of disclosure that the voice's parent held a post in the Hamas-run authority was materially misleading.
"This implied that the public did not have essential details which may have been extremely pertinent to their evaluation of the presenter and the details he provided.
"Credibility is at the center of the bond between a media organization and its public, particularly for a national broadcasting corporation such as the BBC.
"This oversight had the risk to damage the significantly high levels of trust that the public would have placed in a documentary produced by the BBC about the conflict in Gaza."
The documentary was withdrawn from the BBC's streaming service in February after the boy's familial connections emerged, and in the month of July an broadcaster's internal assessment found it breached the corporation's journalistic standards on accuracy.
A representative for the broadcaster said: "The regulator's decision is in agreement with the results of the internal assessment, that there was a serious error in the programme in relation to the BBC's Editorial Guidelines on accuracy, which aligns with Rule 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we comply with the regulator's ruling in its entirety. We will comply with the penalty as soon as the timing and wording are determined."
