The British broadcaster engaged in a "major breach" of media regulations by not revealing that the voice of a film about the Gaza situation was the offspring of a Hamas official, as ruled by UK media regulator Ofcom.
An investigation by the media regulator 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, noting there had been "a significant failing in relation to truthfulness".
Ofcom has ordered the corporation to air a peak-time statement about its findings.
"Given this constitutes a significant violation of our rules, we are ordering the corporation to broadcast a message of our conclusions against it on BBC2 at 9pm, with a date to be finalised," it said.
'Possibility to Erode Credibility'
The watchdog's report stated: "The inquiry we conducted found that the programme's failure to disclose that the narrator's father occupied a role in the Hamas-controlled authority was significantly deceptive.
"It meant that the audience did not have vital facts which may have been highly relevant to their evaluation of the presenter and the details he presented.
"Trust is at the heart of the bond between a media organization and its audience, especially for a state-funded media outlet such as the public broadcaster.
"This error had the possibility to undermine the significantly high levels of confidence that audiences would have placed in a BBC factual programme about the Gaza conflict."
The film 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 determined it breached the broadcaster's editorial guidelines on truthfulness.
A corporation official stated: "The regulator's decision is in line with the results of the internal assessment, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on accuracy, which reflects clause 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we accept the regulator's ruling in complete. We will adhere to the directive as soon as the date and wording are determined."