The public service broadcaster was found to have committed a "major breach" of broadcasting rules by omitting to mention that the presenter of a documentary about the Gaza situation was the child of a Hamas official, as determined by regulatory body Ofcom.
An investigation by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the film was "significantly deceptive".
The BBC's director general had previously apologised, saying there had been "a major oversight in relation to factual correctness".
Ofcom has ordered the corporation to transmit a evening declaration about its conclusions.
"Given this constitutes a significant violation of our regulations, we are ordering the broadcaster to broadcast a announcement of our findings against it on the BBC's second channel at 21:00, with a date to be determined," the statement read.
'Risk to Damage Trust'
The watchdog's report stated: "Our investigation found that the programme's lack of disclosure that the presenter's parent served in a role in the Hamas-controlled administration was significantly deceptive.
"Consequently that the public did not have critical information which may have been extremely pertinent to their evaluation of the presenter and the content he shared.
"Trust is at the heart of the bond between a media organization and its viewers, notably for a state-funded media outlet such as the public broadcaster.
"This oversight had the risk to erode the very considerable levels of confidence that the public would have put in a documentary produced by the BBC about the conflict in Gaza."
The documentary was pulled from the BBC's streaming service in the month of February after the narrator's family links came to light, and in the month of July an internal BBC review found it infringed the corporation's journalistic standards on factual correctness.
A BBC spokesperson said: "The regulator's decision is in agreement with the findings of the internal assessment, that there was a significant failing in the film in relation to the BBC's Editorial Guidelines on truthfulness, which corresponds to regulation 2.2 of the regulator's media standards.
"We expressed regret for this and we agree with the authority's determination in full. We will comply with the directive as soon as the date and wording are finalised."
