The public service broadcaster was found to have committed a "serious breach" of media regulations by omitting to mention that the presenter of a programme about the Gaza conflict was the child of a Hamas representative, according to British broadcasting authority Ofcom.
An inquiry by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the film was "significantly deceptive".
The chief executive of the broadcaster had previously apologised, saying there had been "a serious error in relation to accuracy".
The authority has directed the broadcaster to air a evening statement about its findings.
"Given this constitutes a serious breach of our regulations, we are directing the broadcaster to broadcast a announcement of our findings against it on BBC2 at 21:00, with a timing to be finalised," it said.
'Risk to Erode Trust'
The regulator's report stated: "Our investigation concluded that the film's omission to reveal that the voice's father served in a position in the Hamas-administered administration was substantially inaccurate.
"Consequently that the public did not have essential details which may have been extremely pertinent to their evaluation of the presenter and the content he presented.
"Trust is at the center of the bond between a broadcaster and its public, especially for a state-funded media outlet such as the BBC.
"This failing had the potential to erode the significantly high levels of confidence that the public would have put in a BBC factual programme about the conflict in Gaza."
The documentary was removed from the online platform in February after the narrator's family links emerged, and in July an broadcaster's internal assessment found it infringed the organization's journalistic standards on factual correctness.
A corporation official said: "The authority's determination is in agreement with the results 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 aligns with regulation 2.2 of the regulator's media standards.
"We issued an apology for this and we comply with the regulator's ruling in full. We will follow the penalty as soon as the schedule and wording are finalised."