The public service broadcaster was found to have committed a "major breach" of media regulations by omitting to mention that the voice of a programme about Gaza was the son of a Hamas official, as determined by regulatory body Ofcom.
An inquiry by the media regulator into Gaza: How to Survive a Warzone has found that the programme was "substantially inaccurate".
The BBC's director general had earlier expressed regret, saying there had been "a significant failing in relation to accuracy".
The regulator has ordered the corporation to air a evening statement about its decisions.
"Since this amounts to a major infringement of our rules, we are instructing the BBC to broadcast a announcement of our conclusions against it on the BBC's second channel at nine o'clock in the evening, with a date to be finalised," it said.
'Possibility to Damage Confidence'
The watchdog's report declared: "Our probe concluded that the programme's failure to disclose that the presenter's parent occupied a post in the Hamas-controlled authority was significantly deceptive.
"This implied that the public did not have vital facts which may have been very significant to their assessment of the presenter and the content he shared.
"Confidence is at the heart of the bond between a broadcaster and its audience, especially for a state-funded media outlet such as the public broadcaster.
"This error had the possibility to erode the significantly high amounts of credibility that the public would have put in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was withdrawn from iPlayer in the month of February after the presenter's personal associations emerged, and in July an internal BBC review concluded it infringed the corporation's journalistic standards on truthfulness.
A BBC spokesperson commented: "The regulator's decision is in agreement with the conclusions of the corporation's inquiry, that there was a serious error in the documentary in relation to the broadcaster's journalistic policies on truthfulness, which corresponds to clause 2.2 of the regulator's media standards.
"We have apologised for this and we agree with the regulator's ruling in its entirety. We will adhere to the sanction as soon as the timing and wording are confirmed."
