The public service broadcaster committed a "significant breach" of industry standards by omitting to mention that the voice of a programme about Gaza was the child of a Hamas representative, as ruled by UK media regulator Ofcom.
An inquiry by the media regulator into the documentary titled Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The BBC's director general had already issued an apology, noting there had been "a serious error in relation to factual correctness".
Ofcom has instructed the BBC to broadcast a peak-time announcement about its decisions.
"Since this amounts to a serious breach of our regulations, we are instructing the broadcaster to air a statement of our findings against it on BBC2 at 9pm, with a schedule to be determined," it said.
'Possibility to Damage Trust'
The authority's announcement declared: "Our probe determined that the film's failure to disclose that the presenter's father occupied a role in the Hamas-administered authority was substantially inaccurate.
"It meant that the viewers did not have critical information which may have been extremely pertinent to their assessment of the presenter and the information he presented.
"Credibility is at the core of the connection between a television network and its viewers, particularly for a national broadcasting corporation such as the British Broadcasting Corporation.
"This oversight had the potential to undermine the very considerable levels of confidence that viewers would have placed in a BBC factual programme about the Gaza conflict."
The film was pulled from the BBC's streaming service in February after the boy's familial connections were revealed, and in this past July an corporation's own inquiry concluded it violated the organization's content policies on factual correctness.
A BBC spokesperson said: "The regulator's decision is in line with the results of the corporation's inquiry, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on factual correctness, which aligns with Rule 2.2 of the regulator's media standards.
"We have apologised for this and we accept the authority's determination in its entirety. We will comply with the penalty as soon as the timing and language are determined."
