The public service broadcaster engaged in a "significant breach" of industry standards by omitting to mention that the voice of a documentary about Gaza was the offspring of a Hamas official, according to regulatory body Ofcom.
An inquiry by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the programme was "significantly deceptive".
The BBC's director general had already issued an apology, saying there had been "a serious error in relation to factual correctness".
Ofcom has directed the broadcaster to air a peak-time announcement about its decisions.
"As this represents a major infringement of our rules, we are directing the BBC to transmit a announcement of our findings against it on BBC Two at nine o'clock in the evening, with a schedule to be determined," the regulator stated.
'Potential to Erode Credibility'
The regulator's statement said: "The inquiry we conducted determined that the documentary's failure to disclose that the presenter's father served in a role in the Hamas-run government was significantly deceptive.
"Consequently that the public did not have essential details which may have been extremely pertinent to their assessment of the narrator and the content he presented.
"Confidence is at the core of the connection between a television network and its viewers, notably for a national broadcasting corporation such as the public broadcaster.
"This oversight had the possibility to damage the exceptionally strong degrees of trust that the public would have invested in a factual film from the broadcaster about the Gaza conflict."
The documentary was withdrawn from the BBC's streaming service in the month of February after the boy's family links were revealed, and in July an broadcaster's internal assessment determined it violated the corporation's editorial guidelines on accuracy.
A representative for the broadcaster stated: "The Ofcom ruling is in accordance 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 factual correctness, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we comply with Ofcom's decision in full. We will adhere to the directive as soon as the date and language are determined."