The BBC committed a "significant breach" of industry standards by omitting to mention that the voice of a programme about the Gaza situation was the son of a Hamas representative, as ruled by regulatory body Ofcom.
An probe by Ofcom into Gaza: How to Survive a Warzone has concluded that the documentary was "substantially inaccurate".
The head of the BBC had earlier expressed regret, noting there had been "a significant failing in relation to truthfulness".
The regulator has ordered the broadcaster to air a peak-time statement about its decisions.
"Given this constitutes a major infringement of our rules, we are instructing the corporation to broadcast a announcement of our findings against it on the BBC's second channel at nine o'clock in the evening, with a timing to be determined," the statement read.
'Possibility to Undermine Confidence'
The watchdog's announcement stated: "Our investigation concluded that the documentary's failure to disclose that the voice's father occupied a role in the Hamas-run administration was materially misleading.
"This implied that the viewers did not have vital facts which may have been extremely pertinent to their judgment of the voice and the details he provided.
"Credibility is at the heart of the bond between a television network and its audience, especially for a public service broadcaster such as the public broadcaster.
"This error had the potential to undermine the significantly high levels of confidence that audiences would have invested in a factual film from the broadcaster about the Gaza conflict."
The programme was removed from the online platform in last February after the presenter's family links were revealed, and in the month of July an internal BBC review determined it infringed the corporation's content policies on factual correctness.
A corporation official commented: "The Ofcom ruling is in line with the conclusions of the corporation's inquiry, that there was a serious error in the film in relation to the broadcaster's journalistic policies on accuracy, which corresponds to Rule 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we accept Ofcom's decision in its entirety. We will adhere to the penalty as soon as the timing and wording are determined."
