The public service broadcaster engaged in a "major breach" of industry standards by omitting to mention that the voice of a programme about the Gaza conflict was the child of a Hamas administrator, as determined by British broadcasting authority Ofcom.
An investigation by the media regulator into the documentary titled Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The head of the BBC had earlier expressed regret, stating there had been "a significant failing in relation to accuracy".
The regulator has ordered the broadcaster to air a evening announcement about its decisions.
"As this represents a serious breach of our code, we are instructing the corporation to air a announcement of our determinations against it on BBC Two at 9pm, with a schedule to be determined," it said.
'Possibility to Damage Credibility'
The authority's report stated: "The inquiry we conducted found that the film's failure to disclose that the presenter's male guardian occupied a position in the Hamas-run authority was materially misleading.
"Consequently that the public did not have vital facts which may have been highly relevant to their assessment of the voice and the details he provided.
"Credibility is at the core of the bond between a broadcaster and its viewers, notably for a state-funded media outlet such as the public broadcaster.
"This failing had the potential to erode the very considerable amounts of credibility that viewers would have placed in a BBC factual programme about the Gaza conflict."
The film was removed from iPlayer in last February after the narrator's personal associations came to light, and in July an broadcaster's internal assessment found it violated the corporation's editorial guidelines on factual correctness.
A BBC spokesperson said: "The Ofcom ruling is in line with the conclusions of the corporation's inquiry, that there was a significant failing in the film in relation to the corporation's content standards on accuracy, which reflects Rule 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we accept Ofcom's decision in complete. We will follow the penalty as soon as the schedule and wording are finalised."