The public service broadcaster committed a "significant breach" of broadcasting rules by failing to disclose that the presenter of a programme about the Gaza situation was the offspring of a Hamas representative, as ruled by UK media regulator Ofcom.
An inquiry by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the documentary was "materially misleading".
The BBC's director general had previously apologised, stating there had been "a major oversight in relation to factual correctness".
The authority has directed the corporation to transmit a peak-time declaration about its findings.
"As this represents a significant violation of our code, we are instructing the BBC to air a message of our determinations against it on the BBC's second channel at 9pm, with a timing to be determined," it said.
'Potential to Damage Credibility'
The authority's announcement said: "The inquiry we conducted found that the documentary's failure to disclose that the voice's parent held a position in the Hamas-run authority was substantially inaccurate.
"This implied that the viewers did not have essential details which may have been highly relevant to their judgment of the presenter and the content he provided.
"Confidence is at the center of the bond between a television network and its public, notably for a national broadcasting corporation such as the public broadcaster.
"This error had the risk to damage the very considerable degrees of credibility that audiences would have put in a factual film from the broadcaster about the Gaza conflict."
The programme was removed from iPlayer in last February after the presenter's personal associations came to light, and in July an internal BBC review determined it infringed the corporation's editorial guidelines on factual correctness.
A corporation official said: "The Ofcom ruling is in agreement with the conclusions of Peter Johnston's review, that there was a significant failing in the documentary in relation to the broadcaster's journalistic policies on accuracy, which reflects clause 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we accept the authority's determination in complete. We will comply with the penalty as soon as the schedule and language are finalised."
