The British broadcaster engaged in a "significant breach" of media regulations by omitting to mention that the presenter of a documentary about the Gaza situation was the offspring of a Hamas official, as ruled by British broadcasting authority Ofcom.
An inquiry by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the programme was "materially misleading".
The BBC's director general had earlier expressed regret, noting there had been "a significant failing in relation to factual correctness".
The authority has directed the corporation to air a evening declaration about its findings.
"Given this constitutes a serious breach of our regulations, we are ordering the broadcaster to broadcast a statement of our determinations against it on BBC Two at 9pm, with a date to be confirmed," the regulator stated.
'Risk to Erode Trust'
The authority's report stated: "Our investigation determined that the programme's lack of disclosure that the presenter's male guardian occupied a post in the Hamas-administered government was materially misleading.
"Consequently that the audience did not have vital facts which may have been very significant to their judgment of the narrator and the information he presented.
"Confidence is at the core of the connection between a television network and its public, particularly for a public service broadcaster such as the BBC.
"This oversight had the possibility to erode the very considerable levels of trust that audiences would have invested in a factual film from the broadcaster about the conflict in Gaza."
The film was withdrawn from the BBC's streaming service in last February after the boy's personal associations emerged, and in this past July an corporation's own inquiry concluded it violated the corporation's editorial guidelines on factual correctness.
A BBC spokesperson said: "The authority's determination is in agreement with the findings 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 corresponds to clause 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we comply with the regulator's ruling in its entirety. We will follow the penalty as soon as the schedule and wording are confirmed."