The British broadcaster was found to have committed a "serious breach" of broadcasting rules by not revealing that the voice of a programme about the Gaza conflict was the offspring of a Hamas representative, as ruled by British broadcasting authority Ofcom.
An probe by Ofcom into Gaza: How to Survive a Warzone has found that the programme was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, noting there had been "a significant failing in relation to factual correctness".
The regulator has instructed the broadcaster to broadcast a peak-time declaration about its decisions.
"As this represents a major infringement of our regulations, we are instructing the broadcaster to air a statement of our determinations against it on BBC2 at 9pm, with a timing to be finalised," it said.
'Potential to Undermine Trust'
The authority's report declared: "Our probe found that the film's omission to reveal that the presenter's male guardian served in a position in the Hamas-controlled authority was substantially inaccurate.
"Consequently that the public did not have essential details which may have been highly relevant to their evaluation of the presenter and the information he shared.
"Credibility is at the core of the bond between a broadcaster and its audience, particularly for a state-funded media outlet such as the British Broadcasting Corporation.
"This error had the potential to undermine the very considerable degrees of trust that audiences would have invested in a documentary produced by the BBC about the Gaza conflict."
The film was withdrawn from iPlayer in February after the narrator's familial connections were revealed, and in the month of July an internal BBC review concluded it infringed the organization's editorial guidelines on truthfulness.
A representative for the broadcaster said: "The regulator's decision is in accordance with the results of the corporation's inquiry, that there was a significant failing in the film in relation to the broadcaster's journalistic policies on truthfulness, which aligns with Rule 2.2 of the regulator's media standards.
"We have apologised for this and we comply with Ofcom's decision in full. We will follow the penalty as soon as the timing and language are confirmed."