The public service broadcaster committed a "serious breach" of media regulations by omitting to mention that the voice of a documentary about Gaza was the son of a Hamas representative, as ruled by regulatory body Ofcom.
An probe by the media regulator into the programme Gaza: How to Survive a Warzone has concluded that the programme was "substantially inaccurate".
The BBC's director general had earlier expressed regret, stating there had been "a serious error in relation to truthfulness".
The authority has directed the broadcaster to transmit a evening statement about its decisions.
"Since this amounts to a serious breach of our rules, we are ordering the BBC to broadcast a statement of our findings against it on the BBC's second channel at nine o'clock in the evening, with a schedule to be determined," it said.
'Potential to Erode Trust'
The regulator's report stated: "The inquiry we conducted found that the film's lack of disclosure that the presenter's father occupied a post in the Hamas-run administration was materially misleading.
"This implied that the public did not have critical information which may have been very significant to their evaluation of the narrator and the content he presented.
"Credibility is at the heart of the bond between a television network and its viewers, notably for a national broadcasting corporation such as the public broadcaster.
"This oversight had the potential to damage the very considerable levels of trust that the public would have invested in a documentary produced by the BBC about the Gaza conflict."
The documentary was removed from iPlayer in last February after the boy's personal associations emerged, and in July an internal BBC review concluded it violated the broadcaster's journalistic standards on accuracy.
A BBC spokesperson said: "The Ofcom ruling is in agreement with the results of the internal assessment, that there was a significant failing in the documentary in relation to the corporation's content standards on factual correctness, which corresponds to clause 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with Ofcom's decision in full. We will follow the directive as soon as the timing and wording are confirmed."
