The public service broadcaster was found to have committed a "significant breach" of media regulations by failing to disclose that the voice of a film about the Gaza situation was the son of a Hamas official, according to regulatory body Ofcom.
An probe by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the programme was "materially misleading".
The BBC's director general had earlier expressed regret, saying there had been "a major oversight in relation to accuracy".
Ofcom has directed the corporation to transmit a evening declaration about its findings.
"As this represents a major infringement of our code, we are directing the BBC to transmit a message of our conclusions against it on the BBC's second channel at 9pm, with a schedule to be finalised," the statement read.
'Possibility to Damage Confidence'
The watchdog's statement said: "The inquiry we conducted concluded that the documentary's omission to reveal that the narrator's father occupied a role in the Hamas-administered administration was materially misleading.
"It meant that the audience did not have critical information which may have been highly relevant to their assessment of the presenter and the content he shared.
"Credibility is at the core of the relationship between a broadcaster and its viewers, especially for a public service broadcaster such as the public broadcaster.
"This failing had the potential to damage the significantly high levels of credibility that viewers would have placed in a factual film from the broadcaster about the conflict in Gaza."
The programme was removed from the online platform in February after the boy's familial connections were revealed, and in the month of July an corporation's own inquiry determined it infringed the corporation's content policies on accuracy.
A representative for the broadcaster said: "The authority's determination is in agreement with the findings of Peter Johnston's review, that there was a serious error in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which aligns with regulation 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we agree with the authority's determination in its entirety. We will adhere to the penalty as soon as the schedule and wording are finalised."
