The public service broadcaster engaged in a "significant breach" of industry standards by omitting to mention that the narrator of a programme about Gaza was the son of a Hamas official, as determined by UK media regulator Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has found that the film was "significantly deceptive".
The head of the BBC had previously apologised, saying there had been "a major oversight in relation to truthfulness".
The authority has instructed the corporation to broadcast a prime-time statement about its conclusions.
"Since this amounts to a significant violation of our code, we are ordering the broadcaster to air a message of our findings against it on the BBC's second channel at 9pm, with a timing to be determined," it said.
'Risk to Undermine Trust'
The authority's announcement stated: "Our investigation determined that the film's omission to reveal that the presenter's father occupied a role in the Hamas-run authority was significantly deceptive.
"This implied that the viewers did not have critical information which may have been extremely pertinent to their assessment of the narrator and the details he shared.
"Trust is at the core of the connection between a media organization and its public, particularly for a national broadcasting corporation such as the public broadcaster.
"This failing had the risk to erode the significantly high amounts of trust that audiences would have placed in a BBC factual programme about the conflict in Gaza."
The film was removed from iPlayer in last February after the presenter's family links emerged, and in the month of July an broadcaster's internal assessment found it breached the organization's journalistic standards on accuracy.
A representative for the broadcaster commented: "The Ofcom ruling is in accordance with the findings of Peter Johnston's review, that there was a significant failing in the programme in relation to the broadcaster's journalistic policies on factual correctness, which reflects Rule 2.2 of the regulator's media standards.
"We have apologised for this and we agree with Ofcom's decision in complete. We will adhere to the penalty as soon as the date and wording are finalised."
