The public service broadcaster engaged in a "significant breach" of industry standards by omitting to mention that the voice of a film about the Gaza situation was the child of a Hamas official, according to regulatory body Ofcom.
An investigation by the media regulator into the documentary titled Gaza: How to Survive a Warzone has found 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 directed the broadcaster to transmit a evening declaration about its findings.
"Since this amounts to a major infringement of our rules, we are instructing the broadcaster to transmit a announcement of our conclusions against it on the BBC's second channel at 21:00, with a timing to be confirmed," the regulator stated.
'Possibility to Undermine Trust'
The regulator's statement stated: "Our investigation determined that the documentary's lack of disclosure that the voice's father served in a post in the Hamas-run authority was substantially inaccurate.
"Consequently that the audience did not have vital facts which may have been extremely pertinent to their evaluation of the presenter and the details he provided.
"Trust is at the core of the relationship between a broadcaster and its public, notably for a state-funded media outlet such as the BBC.
"This error had the potential to undermine the very considerable degrees of trust that the public would have put in a documentary produced by the BBC about the Israel-Gaza war."
The documentary was withdrawn from the BBC's streaming service in last February after the boy's personal associations emerged, and in this past July an broadcaster's internal assessment concluded it infringed the corporation's content policies on accuracy.
A corporation official stated: "The authority's determination is in agreement with the findings of the corporation's inquiry, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which corresponds to clause 2.2 of the regulator's media standards.
"We have apologised for this and we comply with the authority's determination in full. We will comply with the sanction as soon as the schedule and wording are confirmed."
