The BBC committed a "serious breach" of industry standards by omitting to mention that the presenter of a programme about the Gaza situation was the offspring of a Hamas official, as determined by British broadcasting authority Ofcom.
An probe by the media regulator into Gaza: How to Survive a Warzone has concluded that the programme was "significantly deceptive".
The BBC's director general had previously apologised, saying there had been "a major oversight in relation to accuracy".
Ofcom has directed the BBC to transmit a prime-time statement about its decisions.
"Since this amounts to a major infringement of our code, we are instructing the broadcaster to air a announcement of our determinations against it on the BBC's second channel at 21:00, with a date to be finalised," it said.
'Risk to Undermine Trust'
The authority's announcement stated: "Our probe found that the programme's lack of disclosure that the narrator's parent held a position in the Hamas-controlled authority was materially misleading.
"It meant that the audience did not have critical information which may have been extremely pertinent to their judgment of the voice and the content he shared.
"Confidence is at the core of the bond between a television network and its audience, particularly for a state-funded media outlet such as the British Broadcasting Corporation.
"This failing had the potential to erode the very considerable degrees of confidence that the public would have put in a documentary produced by the BBC about the Gaza conflict."
The film was removed from the online platform in February after the narrator's family links were revealed, and in July an corporation's own inquiry concluded it breached the broadcaster's journalistic standards on accuracy.
A representative for the broadcaster said: "The Ofcom ruling is in line with the results of the internal assessment, that there was a significant failing in the documentary in relation to the corporation's content standards on accuracy, which reflects regulation 2.2 of the regulator's media standards.
"We issued an apology for this and we accept the authority's determination in complete. We will adhere to the penalty as soon as the schedule and wording are determined."