The public service broadcaster committed a "serious breach" of media regulations by omitting to mention that the voice 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 programme was "substantially inaccurate".
The head of the BBC had previously apologised, saying there had been "a major oversight in relation to truthfulness".
The regulator has instructed the corporation to air a peak-time statement about its findings.
"As this represents a significant violation of our rules, we are instructing the BBC to transmit a announcement of our determinations against it on BBC Two at 21:00, with a schedule to be finalised," the statement read.
'Risk to Erode Confidence'
The authority's report said: "Our investigation concluded that the film's omission to reveal that the presenter's father served in a position in the Hamas-controlled administration was materially misleading.
"This implied that the viewers did not have vital facts which may have been extremely pertinent to their assessment of the presenter and the content he provided.
"Trust is at the center of the bond between a media organization and its viewers, particularly for a national broadcasting corporation such as the BBC.
"This oversight had the possibility to undermine the significantly high degrees of confidence that the public would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was withdrawn from the BBC's streaming service in February after the boy's family links came to light, and in the month of July an internal BBC review determined it violated the broadcaster's editorial guidelines on factual correctness.
A corporation official commented: "The authority's determination is in line with the findings of Peter Johnston's review, that there was a major oversight in the programme in relation to the corporation's content standards on accuracy, which aligns with Rule 2.2 of the regulator's media standards.
"We have apologised for this and we comply with the authority's determination in complete. We will comply with the directive as soon as the date and wording are determined."