The public service broadcaster engaged in a "serious breach" of media regulations by not revealing that the narrator of a programme about Gaza was the offspring of a Hamas representative, as determined by UK media regulator Ofcom.
An probe by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the documentary was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a significant failing in relation to accuracy".
Ofcom has instructed the broadcaster to transmit a evening declaration about its decisions.
"As this represents a significant violation of our code, we are directing the corporation to air a message of our determinations against it on BBC2 at 21:00, with a timing to be finalised," it said.
'Possibility to Damage Confidence'
The authority's announcement stated: "Our probe found that the documentary's failure to disclose that the voice's male guardian served in a post in the Hamas-administered administration was materially misleading.
"This implied that the viewers did not have critical information which may have been extremely pertinent to their assessment of the presenter and the details he provided.
"Trust is at the core of the connection between a broadcaster and its public, especially for a national broadcasting corporation such as the public broadcaster.
"This oversight had the risk to damage the significantly high amounts of credibility that the public would have placed in a documentary produced by the BBC about the conflict in Gaza."
The documentary was withdrawn from iPlayer in February after the boy's personal associations were revealed, and in the month of July an broadcaster's internal assessment concluded it breached the organization's editorial guidelines on truthfulness.
A corporation official said: "The Ofcom ruling is in line with the conclusions of Peter Johnston's review, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on factual correctness, which aligns with clause 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we comply with the regulator's ruling in its entirety. We will comply with the penalty as soon as the date and wording are confirmed."