The public service broadcaster committed a "major breach" of broadcasting rules by omitting to mention that the voice of a documentary about the Gaza situation was the offspring of a Hamas official, as determined by British broadcasting authority Ofcom.
An investigation by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has concluded that the programme was "materially misleading".
The BBC's director general had earlier expressed regret, saying there had been "a major oversight in relation to truthfulness".
The authority has ordered the corporation to transmit a evening statement about its decisions.
"Given this constitutes a significant violation of our rules, we are directing the BBC to air a statement of our conclusions against it on BBC Two at 21:00, with a date to be determined," it said.
'Possibility to Erode Confidence'
The authority's announcement declared: "Our investigation found that the programme's failure to disclose that the narrator's father occupied a post in the Hamas-run authority was materially misleading.
"This implied that the public did not have essential details which may have been highly relevant to their judgment of the narrator and the content he provided.
"Credibility is at the heart of the connection between a broadcaster and its public, especially for a public service broadcaster such as the BBC.
"This error had the potential to erode the exceptionally strong amounts of trust that the public would have put in a factual film from the broadcaster about the Gaza conflict."
The programme was withdrawn from iPlayer in the month of February after the presenter's personal associations came to light, and in this past July an broadcaster's internal assessment determined it infringed the corporation's content policies on accuracy.
A BBC spokesperson commented: "The regulator's decision is in line with the findings of Peter Johnston's review, that there was a significant failing in the programme in relation to the corporation's content standards on truthfulness, which corresponds to regulation 2.2 of the authority's broadcasting regulations.
"We expressed regret for this and we agree with Ofcom's decision in full. We will adhere to the penalty as soon as the timing and language are confirmed."
