The British broadcaster engaged in a "significant breach" of industry standards by omitting to mention that the narrator of a programme about Gaza was the child of a Hamas administrator, as ruled by regulatory body Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has determined that the documentary was "significantly deceptive".
The BBC's director general had previously apologised, noting there had been "a significant failing in relation to factual correctness".
Ofcom has directed the corporation to broadcast a peak-time announcement about its findings.
"Given this constitutes a significant violation of our rules, we are ordering the broadcaster to broadcast a statement of our findings against it on BBC2 at 21:00, with a timing to be confirmed," it said.
The authority's announcement declared: "Our probe found that the documentary's failure to disclose that the presenter's male guardian occupied a post in the Hamas-run authority was substantially inaccurate.
"Consequently that the public did not have essential details which may have been highly relevant to their assessment of the presenter and the content he presented.
"Credibility is at the heart of the bond between a media organization and its audience, particularly for a state-funded media outlet such as the public broadcaster.
"This oversight had the potential to erode the significantly high degrees of trust that the public would have invested in a factual film from the broadcaster about the conflict in Gaza."
The programme was withdrawn from iPlayer in February after the narrator's familial connections came to light, and in the month of July an broadcaster's internal assessment determined it infringed the corporation's content policies on factual correctness.
A corporation official said: "The Ofcom ruling is in agreement with the findings of the corporation's inquiry, that there was a major oversight in the documentary in relation to the corporation's content standards on truthfulness, which reflects regulation 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with Ofcom's decision in complete. We will comply with the sanction as soon as the schedule and wording are confirmed."