The public service broadcaster committed a "serious breach" of broadcasting rules by omitting to mention that the voice of a programme about the Gaza situation was the son of a Hamas administrator, according to British broadcasting authority Ofcom.
An probe by the media regulator into the documentary titled Gaza: How to Survive a Warzone has determined that the programme was "substantially inaccurate".
The chief executive of the broadcaster had previously apologised, saying there had been "a serious error in relation to truthfulness".
The authority has directed the corporation to air a prime-time statement about its findings.
"As this represents a significant violation of our regulations, we are ordering the broadcaster to broadcast a statement of our findings against it on BBC Two at nine o'clock in the evening, with a schedule to be determined," it said.
'Possibility to Erode Credibility'
The regulator's report stated: "The inquiry we conducted found that the documentary's lack of disclosure that the presenter's parent held a post in the Hamas-controlled administration was materially misleading.
"Consequently that the viewers did not have critical information which may have been very significant to their assessment of the voice and the information he presented.
"Confidence is at the core of the connection between a media organization and its public, particularly for a state-funded media outlet such as the BBC.
"This error had the potential to undermine the exceptionally strong degrees of trust that audiences would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The programme was removed from the BBC's streaming service in last February after the boy's family links came to light, and in this past July an corporation's own inquiry concluded it infringed the organization's journalistic standards on accuracy.
A representative for the broadcaster said: "The authority's determination is in agreement with the results of Peter Johnston's review, that there was a major oversight in the documentary in relation to the corporation's content standards on factual correctness, which reflects regulation 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we agree with the authority's determination in its entirety. We will adhere to the directive as soon as the timing and language are finalised."