The public service broadcaster was found to have committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a programme about the Gaza situation was the son of a Hamas official, according to UK media regulator Ofcom.
An probe by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the documentary was "substantially inaccurate".
The head of the BBC had previously apologised, saying there had been "a significant failing in relation to accuracy".
The authority has directed the BBC to transmit a prime-time declaration about its conclusions.
"As this represents a serious breach of our code, we are instructing the corporation to broadcast a message of our conclusions against it on BBC2 at 21:00, with a date to be determined," the regulator stated.
'Potential to Undermine Credibility'
The authority's announcement stated: "Our investigation determined that the programme's omission to reveal that the narrator's parent held a post in the Hamas-controlled authority was materially misleading.
"Consequently that the public did not have critical information which may have been extremely pertinent to their evaluation of the voice and the details he shared.
"Trust is at the core of the connection between a media organization and its viewers, particularly for a national broadcasting corporation such as the public broadcaster.
"This oversight had the potential to damage the significantly high degrees of trust that viewers would have put in a factual film from the broadcaster about the conflict in Gaza."
The documentary was withdrawn from iPlayer in last February after the boy's family links were revealed, and in July an internal BBC review found it infringed the corporation's content policies on accuracy.
A BBC spokesperson stated: "The regulator's decision is in line with the findings of the corporation's inquiry, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on factual correctness, which corresponds to clause 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with the authority's determination in complete. We will follow the penalty as soon as the date and language are finalised."
