The public service broadcaster committed a "significant breach" of broadcasting rules by omitting to mention that the voice of a film about Gaza was the son of a Hamas official, as determined by UK media regulator Ofcom.
An probe by Ofcom into Gaza: How to Survive a Warzone has found that the film was "substantially inaccurate".
The head of the BBC had previously apologised, saying there had been "a serious error in relation to truthfulness".
The authority has ordered the corporation to air a peak-time statement about its decisions.
"Given this constitutes a significant violation of our code, we are directing the broadcaster to transmit a message of our conclusions against it on BBC Two at 9pm, with a date to be determined," the regulator stated.
'Risk to Undermine Trust'
The watchdog's announcement said: "Our investigation concluded that the documentary's omission to reveal that the narrator's father served in a role in the Hamas-controlled authority was substantially inaccurate.
"This implied that the public did not have vital facts which may have been extremely pertinent to their evaluation of the presenter and the information he provided.
"Credibility is at the heart of the connection between a broadcaster and its viewers, notably for a public service broadcaster such as the public broadcaster.
"This failing had the potential to damage the significantly high degrees of credibility that viewers would have put in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was removed from the online platform in the month of February after the boy's personal associations emerged, and in the month of July an corporation's own inquiry concluded it breached the broadcaster's content policies on truthfulness.
A corporation official said: "The Ofcom ruling is in accordance with the conclusions of the corporation's inquiry, that there was a serious error in the programme in relation to the BBC's Editorial Guidelines on truthfulness, which corresponds to regulation 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we comply with Ofcom's decision in full. We will comply with the penalty as soon as the timing and wording are confirmed."
