The British broadcaster was found to have committed a "significant breach" of media regulations by failing to disclose that the voice of a programme about the Gaza conflict was the child of a Hamas administrator, according to regulatory body Ofcom.
An inquiry by the media regulator into the programme Gaza: How to Survive a Warzone has found that the film was "materially misleading".
The BBC's director general had earlier expressed regret, saying there had been "a serious error in relation to truthfulness".
Ofcom has ordered the BBC to air a evening statement about its decisions.
"Given this constitutes a serious breach of our regulations, we are directing the BBC to broadcast a message of our findings against it on BBC2 at 21:00, with a date to be determined," it said.
'Risk to Undermine Trust'
The authority's announcement stated: "Our probe concluded that the film's lack of disclosure that the presenter's parent held a post in the Hamas-run government was materially misleading.
"It meant that the audience did not have vital facts which may have been highly relevant to their judgment of the voice and the content he provided.
"Trust is at the core of the connection between a broadcaster and its public, especially for a national broadcasting corporation such as the public broadcaster.
"This oversight had the risk to undermine the significantly high amounts of trust that viewers would have invested in a factual film from the broadcaster about the Gaza conflict."
The documentary was pulled from iPlayer in last February after the boy's familial connections emerged, and in July an broadcaster's internal assessment concluded it violated the broadcaster's content policies on factual correctness.
A corporation official stated: "The regulator's decision is in agreement with the conclusions of Peter Johnston's review, that there was a serious error in the film in relation to the corporation's content standards on factual correctness, which aligns with regulation 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with the authority's determination in its entirety. We will follow the penalty as soon as the date and wording are determined."
