The public service broadcaster engaged in a "major breach" of industry standards by failing to disclose that the narrator of a programme about the Gaza situation was the child of a Hamas representative, as determined by British broadcasting authority Ofcom.
An inquiry by Ofcom into the programme Gaza: How to Survive a Warzone has found that the documentary was "materially misleading".
The head of the BBC had previously apologised, saying there had been "a major oversight in relation to accuracy".
The regulator has directed the BBC to air a prime-time statement about its findings.
"Given this constitutes a major infringement of our regulations, we are directing the corporation to broadcast a announcement of our findings against it on the BBC's second channel at 21:00, with a date to be confirmed," the statement read.
'Risk to Undermine Credibility'
The regulator's announcement said: "Our probe found that the film's failure to disclose that the voice's parent served in a role in the Hamas-run government was materially misleading.
"This implied that the audience did not have vital facts which may have been extremely pertinent to their evaluation of the narrator and the information he presented.
"Trust is at the center of the connection between a media organization and its public, notably for a public service broadcaster such as the British Broadcasting Corporation.
"This error had the potential to damage the exceptionally strong amounts of trust that the public would have invested in a BBC factual programme about the Israel-Gaza war."
The documentary was removed from the online platform in last February after the boy's familial connections came to light, and in July an broadcaster's internal assessment concluded it breached the organization's content policies on factual correctness.
A representative for the broadcaster said: "The regulator's decision is in line with the results of Peter Johnston's review, that there was a significant failing in the programme in relation to the broadcaster's journalistic policies on accuracy, which reflects clause 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with the regulator's ruling in complete. We will comply with the penalty as soon as the timing and language are determined."
