The public service broadcaster was found to have committed a "major breach" of media regulations by failing to disclose that the voice of a programme about Gaza was the offspring of a Hamas official, as ruled by UK media regulator Ofcom.
An inquiry by Ofcom into the documentary titled Gaza: How to Survive a Warzone has concluded that the documentary was "substantially inaccurate".
The BBC's director general had earlier expressed regret, saying there had been "a serious error in relation to accuracy".
The authority has ordered the BBC to transmit a prime-time announcement about its decisions.
"As this represents a serious breach of our rules, we are instructing the corporation to broadcast a announcement of our determinations against it on BBC Two at nine o'clock in the evening, with a date to be finalised," it said.
'Risk to Erode Credibility'
The watchdog's statement declared: "Our probe concluded that the programme's omission to reveal that the presenter's male guardian occupied a position in the Hamas-run administration was significantly deceptive.
"It meant that the viewers did not have essential details which may have been very significant to their judgment of the presenter and the information he presented.
"Confidence is at the heart of the relationship between a television network and its public, especially for a public service broadcaster such as the public broadcaster.
"This error had the potential to undermine the very considerable degrees of credibility that the public would have placed in a BBC factual programme about the conflict in Gaza."
The documentary was pulled from iPlayer in the month of February after the boy's family links came to light, and in the month of July an broadcaster's internal assessment concluded it infringed the broadcaster's editorial guidelines on accuracy.
A representative for the broadcaster stated: "The regulator's decision is in line with the conclusions of Peter Johnston's review, that there was a major oversight in the programme in relation to the corporation's content standards on accuracy, which reflects Rule 2.2 of Ofcom's Broadcasting Code.
"We issued an apology for this and we agree with the regulator's ruling in full. We will adhere to the penalty as soon as the timing and wording are confirmed."
