The public service broadcaster committed a "significant breach" of industry standards by omitting to mention that the voice of a documentary about Gaza was the offspring of a Hamas official, as ruled by British broadcasting authority Ofcom.
An inquiry by Ofcom into Gaza: How to Survive a Warzone has concluded that the programme was "substantially inaccurate".
The head of the BBC had already issued an apology, saying there had been "a significant failing in relation to accuracy".
Ofcom has instructed the BBC to broadcast a prime-time declaration about its decisions.
"As this represents a major infringement of our code, we are directing the broadcaster to air a statement of our determinations against it on BBC Two at nine o'clock in the evening, with a schedule to be determined," it said.
'Possibility to Damage Confidence'
The regulator's report stated: "Our investigation concluded that the programme's failure to disclose that the presenter's father served in a role in the Hamas-run authority was significantly deceptive.
"Consequently that the audience did not have essential details which may have been very significant to their evaluation of the voice and the information he presented.
"Confidence is at the heart of the relationship between a broadcaster and its public, notably for a public service broadcaster such as the public broadcaster.
"This oversight had the possibility to undermine the significantly high degrees of trust that viewers would have placed in a factual film from the broadcaster about the Israel-Gaza war."
The documentary was removed from iPlayer in February after the boy's personal associations were revealed, and in the month of July an broadcaster's internal assessment concluded it infringed the broadcaster's content policies on factual correctness.
A corporation official stated: "The authority's determination is in line with the results of Peter Johnston's review, that there was a serious error in the documentary in relation to the broadcaster's journalistic policies on factual correctness, which reflects Rule 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with Ofcom's decision in complete. We will adhere to the penalty as soon as the schedule and wording are determined."
