The public service broadcaster was found to have committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a documentary about the Gaza conflict was the offspring of a Hamas official, as determined by regulatory body Ofcom.
An inquiry by the media regulator into the documentary titled Gaza: How to Survive a Warzone has determined that the film was "significantly deceptive".
The head of the BBC had earlier expressed regret, noting there had been "a serious error in relation to truthfulness".
The authority has directed the broadcaster to broadcast a evening announcement about its decisions.
"Since this amounts to a major infringement of our regulations, we are ordering the BBC to transmit a message of our determinations against it on BBC Two at nine o'clock in the evening, with a schedule to be finalised," it said.
'Possibility to Erode Trust'
The watchdog's statement declared: "The inquiry we conducted found that the programme's failure to disclose that the narrator's father occupied a role in the Hamas-run government was significantly deceptive.
"This implied that the viewers did not have essential details which may have been very significant to their judgment of the voice and the details he shared.
"Trust is at the heart of the connection between a media organization and its public, particularly for a public service broadcaster such as the public broadcaster.
"This failing had the potential to damage the exceptionally strong degrees of credibility that the public would have placed in a documentary produced by the BBC about the Gaza conflict."
The documentary was pulled from the BBC's streaming service in the month of February after the boy's personal associations were revealed, and in the month of July an internal BBC review concluded it infringed the organization's content policies on truthfulness.
A representative for the broadcaster stated: "The authority's determination is in line with the conclusions of Peter Johnston's review, that there was a significant failing in the film in relation to the broadcaster's journalistic policies on factual correctness, which reflects Rule 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with Ofcom's decision in its entirety. We will adhere to the penalty as soon as the date and wording are finalised."