The BBC was found to have committed a "major breach" of broadcasting rules by not revealing that the voice of a documentary about the Gaza situation was the son of a Hamas representative, as determined by British broadcasting authority Ofcom.
An probe by the media regulator into the programme Gaza: How to Survive a Warzone has determined that the documentary was "materially misleading".
The BBC's director general had already issued an apology, noting there had been "a serious error in relation to factual correctness".
Ofcom has ordered the broadcaster to transmit a peak-time declaration about its findings.
"Since this amounts to a major infringement of our rules, we are instructing the corporation to broadcast a message of our conclusions against it on BBC2 at 9pm, with a timing to be confirmed," it said.
'Possibility to Damage Trust'
The authority's announcement stated: "Our investigation concluded that the film's failure to disclose that the presenter's parent held a post in the Hamas-controlled authority was substantially inaccurate.
"This implied that the viewers did not have critical information which may have been extremely pertinent to their assessment of the voice and the details he presented.
"Confidence is at the center of the connection between a television network and its audience, notably for a national broadcasting corporation such as the BBC.
"This oversight had the risk to erode the exceptionally strong levels of confidence that audiences would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The programme was withdrawn from the BBC's streaming service in last February after the presenter's family links were revealed, and in July an broadcaster's internal assessment concluded it violated the corporation's content policies on truthfulness.
A BBC spokesperson commented: "The authority's determination is in agreement with the findings of Peter Johnston's review, that there was a major oversight in the documentary in relation to the corporation's content standards on factual correctness, which aligns with clause 2.2 of the regulator's media standards.
"We expressed regret for this and we accept the authority's determination in its entirety. We will comply with the penalty as soon as the schedule and wording are determined."