The public service broadcaster was found to have committed a "major breach" of industry standards by not revealing that the voice of a programme about Gaza was the child of a Hamas representative, as determined by UK media regulator Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has found that the documentary was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a major oversight in relation to accuracy".
The authority has instructed the BBC to broadcast a peak-time announcement about its conclusions.
"Since this amounts to a serious breach of our regulations, we are instructing the broadcaster to transmit a message of our determinations against it on BBC2 at 21:00, with a date to be determined," it said.
'Potential to Damage Credibility'
The regulator's announcement declared: "The inquiry we conducted found that the programme's omission to reveal that the voice's male guardian held a post in the Hamas-controlled government was substantially inaccurate.
"This implied that the public did not have vital facts which may have been extremely pertinent to their assessment of the presenter and the content he provided.
"Confidence is at the center of the connection between a broadcaster and its audience, particularly for a state-funded media outlet such as the BBC.
"This error had the possibility to damage the significantly high levels of trust that viewers would have placed in a documentary produced by the BBC about the Gaza conflict."
The film was removed from the BBC's streaming service in February after the narrator's familial connections emerged, and in this past July an corporation's own inquiry found it violated the broadcaster's editorial guidelines on truthfulness.
A corporation official said: "The regulator's decision is in line with the conclusions of the corporation's inquiry, that there was a major oversight in the programme in relation to the broadcaster's journalistic policies on factual correctness, which aligns with clause 2.2 of the regulator's media standards.
"We issued an apology for this and we accept Ofcom's decision in complete. We will adhere to the penalty as soon as the schedule and language are determined."
