The public service broadcaster engaged in a "serious breach" of broadcasting rules by failing to disclose that the voice of a programme about the Gaza conflict was the offspring of a Hamas administrator, as ruled by UK media regulator Ofcom.
An investigation by Ofcom into Gaza: How to Survive a Warzone has concluded that the film was "materially misleading".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a serious error in relation to accuracy".
The regulator has instructed the broadcaster to broadcast a prime-time statement about its conclusions.
"Since this amounts to a significant violation of our code, we are instructing the corporation to broadcast a message of our conclusions against it on BBC Two at 21:00, with a timing to be determined," the statement read.
'Risk to Damage Credibility'
The regulator's statement stated: "Our investigation determined that the documentary's lack of disclosure that the presenter's male guardian held a role in the Hamas-run administration was significantly deceptive.
"It meant that the viewers did not have vital facts which may have been extremely pertinent to their judgment of the presenter and the details he shared.
"Trust is at the core of the connection between a television network and its viewers, especially for a national broadcasting corporation such as the public broadcaster.
"This error had the potential to erode the very considerable amounts of trust that audiences would have invested in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was withdrawn from iPlayer in last February after the boy's familial connections emerged, and in the month of July an broadcaster's internal assessment concluded it violated the organization's content policies on factual correctness.
A corporation official commented: "The regulator's decision is in agreement with the results of Peter Johnston's review, that there was a significant failing in the film in relation to the corporation's content standards on factual correctness, which aligns with Rule 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we accept Ofcom's decision in complete. We will comply with the penalty as soon as the schedule and wording are confirmed."
