The public service broadcaster engaged in a "major breach" of industry standards by omitting to mention that the voice of a film about the Gaza situation was the child of a Hamas administrator, as ruled by regulatory body Ofcom.
An probe by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The chief executive of the broadcaster had previously apologised, saying there had been "a major oversight in relation to factual correctness".
The authority has directed the BBC to transmit a evening announcement about its findings.
"As this represents a serious breach of our code, we are instructing the corporation to air a statement of our findings against it on BBC2 at 9pm, with a schedule to be determined," the regulator stated.
'Possibility to Erode Trust'
The watchdog's report declared: "Our investigation determined that the film's failure to disclose that the voice's father held a position in the Hamas-administered administration was significantly deceptive.
"It meant that the viewers did not have essential details which may have been extremely pertinent to their judgment of the narrator and the content he provided.
"Trust is at the core of the connection between a television network and its viewers, especially for a national broadcasting corporation such as the BBC.
"This error had the possibility to erode the significantly high degrees of trust that viewers would have put in a BBC factual programme about the Gaza conflict."
The documentary was removed from the BBC's streaming service in the month of February after the boy's familial connections were revealed, and in July an broadcaster's internal assessment concluded it breached the organization's editorial guidelines on accuracy.
A BBC spokesperson said: "The regulator's decision is in agreement with the results of the corporation's inquiry, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on accuracy, which reflects clause 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we accept the authority's determination in full. We will comply with the penalty as soon as the schedule and wording are confirmed."