The public service broadcaster engaged in a "major breach" of broadcasting rules by omitting to mention that the voice of a programme about the Gaza conflict was the son of a Hamas administrator, as determined by regulatory body Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the programme was "substantially inaccurate".
The head of the BBC had already issued an apology, stating there had been "a major oversight in relation to factual correctness".
The regulator has instructed the corporation to air a prime-time statement about its decisions.
"Given this constitutes a serious breach of our regulations, we are directing the broadcaster to transmit a statement of our findings against it on BBC2 at 9pm, with a date to be confirmed," the statement read.
'Potential to Erode Trust'
The regulator's report stated: "Our investigation concluded that the film's lack of disclosure that the voice's father occupied a role in the Hamas-administered government was significantly deceptive.
"It meant that the viewers did not have essential details which may have been highly relevant to their assessment of the narrator and the content he shared.
"Confidence is at the heart of the relationship between a media organization and its public, especially for a national broadcasting corporation such as the public broadcaster.
"This failing had the potential to erode the significantly high amounts of credibility that viewers would have put in a BBC factual programme about the Gaza conflict."
The film was removed from the BBC's streaming service in last February after the boy's family links emerged, and in the month of July an corporation's own inquiry concluded it violated the corporation's journalistic standards on truthfulness.
A representative for the broadcaster said: "The Ofcom ruling is in line with the results of the corporation's inquiry, that there was a serious error in the film in relation to the corporation's content standards on factual correctness, which corresponds to clause 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we accept the regulator's ruling in complete. We will comply with the penalty as soon as the schedule and wording are finalised."
