The British broadcaster engaged in a "serious breach" of media regulations by omitting to mention that the voice of a programme about Gaza was the son of a Hamas administrator, as ruled by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the documentary was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, stating there had been "a serious error in relation to factual correctness".
Ofcom has instructed the broadcaster to air a evening announcement about its conclusions.
"As this represents a major infringement of our regulations, we are directing the broadcaster to air a announcement of our determinations against it on BBC Two at nine o'clock in the evening, with a timing to be finalised," it said.
'Risk to Erode Credibility'
The authority's report said: "Our probe determined that the film's omission to reveal that the voice's male guardian held a role in the Hamas-controlled authority was substantially inaccurate.
"It meant that the viewers did not have essential details which may have been highly relevant to their assessment of the voice and the details he shared.
"Trust is at the center of the bond between a broadcaster and its viewers, particularly for a national broadcasting corporation such as the public broadcaster.
"This oversight had the possibility to damage the very considerable degrees of trust that viewers would have put in a factual film from the broadcaster about the Gaza conflict."
The documentary was pulled from the BBC's streaming service in February after the boy's personal associations emerged, and in the month of July an internal BBC review concluded it violated the organization's content policies on factual correctness.
A representative for the broadcaster commented: "The regulator's decision is in accordance with the conclusions of Peter Johnston's review, that there was a significant failing in the programme in relation to the BBC's Editorial Guidelines on factual correctness, which aligns with Rule 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we agree with the authority's determination in its entirety. We will follow the penalty as soon as the timing and wording are determined."