The British broadcaster committed a "major breach" of industry standards by failing to disclose that the presenter of a programme about the Gaza situation was the offspring of a Hamas representative, as ruled by regulatory body Ofcom.
An inquiry by Ofcom into the programme Gaza: How to Survive a Warzone has concluded that the programme was "materially misleading".
The BBC's director general had already issued an apology, stating there had been "a significant failing in relation to truthfulness".
The regulator has directed the broadcaster to transmit a prime-time statement about its decisions.
"Since this amounts to a major infringement of our code, we are directing the corporation to transmit a announcement of our findings against it on BBC Two at 21:00, with a timing to be finalised," it said.
'Potential to Damage Trust'
The authority's announcement declared: "Our probe concluded that the documentary's lack of disclosure that the voice's parent held a role in the Hamas-run authority was materially misleading.
"This implied that the viewers did not have essential details which may have been highly relevant to their assessment of the presenter and the content he provided.
"Credibility is at the center of the relationship between a television network and its viewers, notably for a state-funded media outlet such as the public broadcaster.
"This error had the potential to undermine the significantly high degrees of trust that the public would have put in a documentary produced by the BBC about the conflict in Gaza."
The documentary was withdrawn from the BBC's streaming service in February after the narrator's familial connections emerged, and in July an internal BBC review determined it infringed the corporation's editorial guidelines on accuracy.
A BBC spokesperson said: "The Ofcom ruling is in line with the results of the corporation's inquiry, that there was a serious error in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which reflects regulation 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we accept the authority's determination in full. We will adhere to the penalty as soon as the date and wording are determined."