The British broadcaster engaged in a "serious breach" of media regulations by omitting to mention that the voice of a documentary about the Gaza situation was the offspring of a Hamas administrator, as ruled by UK media regulator Ofcom.
An investigation by Ofcom into the programme Gaza: How to Survive a Warzone has determined that the film was "substantially inaccurate".
The BBC's director general had already issued an apology, saying there had been "a major oversight in relation to factual correctness".
The authority has directed the broadcaster to air a peak-time declaration about its conclusions.
"Given this constitutes a significant violation of our code, we are directing the BBC to transmit a statement of our determinations against it on BBC2 at 9pm, with a timing to be finalised," the regulator stated.
'Potential to Undermine Trust'
The authority's statement declared: "The inquiry we conducted found that the film's omission to reveal that the voice's father served in a position in the Hamas-controlled government was significantly deceptive.
"This implied that the viewers did not have vital facts which may have been highly relevant to their evaluation of the voice and the content he presented.
"Confidence is at the core of the connection between a broadcaster and its viewers, particularly for a national broadcasting corporation such as the BBC.
"This oversight had the possibility to erode the exceptionally strong amounts of confidence that the public would have put in a factual film from the broadcaster about the Gaza conflict."
The programme was removed from the online platform in last February after the boy's familial connections came to light, and in this past July an internal BBC review concluded it breached the corporation's journalistic standards on factual correctness.
A representative for the broadcaster commented: "The Ofcom ruling is in accordance with the results of the internal assessment, that there was a serious error in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which corresponds to clause 2.2 of the regulator's media standards.
"We issued an apology for this and we accept the authority's determination in its entirety. We will comply with the penalty as soon as the schedule and wording are finalised."