The public service broadcaster was found to have committed a "serious breach" of broadcasting rules by omitting to mention that the narrator of a programme about the Gaza situation was the offspring of a Hamas representative, as ruled by UK media regulator Ofcom.
An investigation by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has found that the documentary was "significantly deceptive".
The BBC's director general had already issued an apology, saying there had been "a significant failing in relation to factual correctness".
Ofcom has ordered the BBC to broadcast a peak-time announcement about its conclusions.
"Since this amounts to a major infringement of our regulations, we are instructing the broadcaster to broadcast a message of our conclusions against it on the BBC's second channel at 9pm, with a timing to be finalised," it said.
'Potential to Undermine Trust'
The authority's statement stated: "Our probe determined that the documentary's failure to disclose that the narrator's parent occupied a post in the Hamas-run authority was materially misleading.
"It meant that the viewers did not have critical information which may have been very significant to their evaluation of the presenter and the information he shared.
"Trust is at the core of the relationship between a broadcaster and its viewers, especially for a state-funded media outlet such as the BBC.
"This error had the possibility to damage the very considerable degrees of trust that the public would have invested in a BBC factual programme about the conflict in Gaza."
The documentary was withdrawn from the BBC's streaming service in February after the presenter's family links came to light, and in the month of July an broadcaster's internal assessment found it breached the broadcaster's content policies on factual correctness.
A corporation official said: "The regulator's decision is in line with the results of the internal assessment, that there was a major oversight in the film in relation to the BBC's Editorial Guidelines on factual correctness, which reflects clause 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with the regulator's ruling in full. We will follow the penalty as soon as the timing and language are confirmed."
