The public service broadcaster engaged in a "serious breach" of media regulations by omitting to mention that the presenter of a programme about the Gaza conflict was the offspring of a Hamas administrator, as determined by regulatory body Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has concluded that the film was "significantly deceptive".
The BBC's director general had already issued an apology, saying there had been "a serious error in relation to accuracy".
Ofcom has ordered the corporation to air a evening statement about its conclusions.
"Given this constitutes a serious breach of our rules, we are instructing the corporation to transmit a announcement of our conclusions against it on BBC Two at nine o'clock in the evening, with a date to be finalised," the regulator stated.
'Potential to Undermine Trust'
The authority's announcement said: "Our probe determined that the programme's lack of disclosure that the presenter's father occupied a role in the Hamas-administered authority was significantly deceptive.
"This implied that the audience did not have vital facts which may have been extremely pertinent to their assessment of the voice and the content he provided.
"Confidence is at the center of the bond between a television network and its public, especially for a state-funded media outlet such as the public broadcaster.
"This failing had the risk to erode the exceptionally strong degrees of credibility that viewers would have put in a documentary produced by the BBC about the conflict in Gaza."
The programme was removed from the BBC's streaming service in the month of February after the boy's personal associations came to light, and in July an broadcaster's internal assessment determined it violated the broadcaster's editorial guidelines on truthfulness.
A representative for the broadcaster stated: "The authority's determination is in line with the results of the internal assessment, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on truthfulness, which corresponds to regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we accept the regulator's ruling in full. We will follow the directive as soon as the schedule and wording are finalised."