The BBC engaged in a "significant breach" of industry standards by omitting to mention that the voice of a programme about the Gaza conflict was the son of a Hamas representative, as determined by regulatory body Ofcom.
An probe by Ofcom into Gaza: How to Survive a Warzone has concluded that the programme was "substantially inaccurate".
The head of the BBC had earlier expressed regret, noting there had been "a major oversight in relation to truthfulness".
The regulator has directed the BBC to air a evening announcement about its conclusions.
"Given this constitutes a major infringement of our rules, we are ordering the corporation to broadcast a announcement of our conclusions against it on BBC2 at 21:00, with a schedule to be confirmed," it said.
'Risk to Undermine Confidence'
The regulator's statement declared: "Our investigation concluded that the documentary's omission to reveal that the voice's parent served in a role in the Hamas-run authority was materially misleading.
"This implied that the viewers did not have essential details which may have been extremely pertinent to their judgment of the presenter and the information he shared.
"Trust is at the center of the relationship between a broadcaster and its viewers, especially for a national broadcasting corporation such as the BBC.
"This error had the possibility to damage the very considerable amounts of confidence that audiences would have put in a BBC factual programme about the Gaza conflict."
The programme was removed from the BBC's streaming service in last February after the boy's family links emerged, and in July an corporation's own inquiry determined it violated the corporation's content policies on accuracy.
A corporation official stated: "The Ofcom ruling is in agreement with the conclusions of the corporation's inquiry, that there was a significant failing in the film in relation to the broadcaster's journalistic policies on accuracy, which reflects Rule 2.2 of the regulator's media standards.
"We issued an apology for this and we comply with the regulator's ruling in its entirety. We will follow the penalty as soon as the schedule and wording are finalised."
