The public service broadcaster committed a "significant breach" of industry standards by omitting to mention that the narrator of a programme about the Gaza situation was the offspring of a Hamas administrator, as determined by British broadcasting authority Ofcom.
An probe by the media regulator into Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The BBC's director general had previously apologised, saying there had been "a major oversight in relation to factual correctness".
The regulator has directed the BBC to transmit a peak-time statement about its findings.
"Given this constitutes a major infringement of our rules, we are ordering the broadcaster to broadcast a message of our conclusions against it on BBC Two at 21:00, with a schedule to be determined," the statement read.
'Risk to Damage Trust'
The authority's announcement said: "Our probe concluded that the documentary's lack of disclosure that the narrator's father held a role in the Hamas-controlled authority was significantly deceptive.
"Consequently that the viewers did not have vital facts which may have been highly relevant to their assessment of the narrator and the content he shared.
"Confidence is at the center of the bond between a broadcaster and its viewers, especially for a national broadcasting corporation such as the BBC.
"This oversight had the potential to undermine the very considerable levels of trust that viewers would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The documentary was removed from the online platform in last February after the narrator's family links came to light, and in the month of July an internal BBC review concluded it breached the corporation's journalistic standards on truthfulness.
A BBC spokesperson commented: "The regulator's decision is in line with the findings of the internal assessment, that there was a major oversight in the documentary in relation to the broadcaster's journalistic policies on factual correctness, which aligns with Rule 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with Ofcom's decision in full. We will adhere to the penalty as soon as the timing and language are determined."