The public service broadcaster was found to have committed a "significant breach" of media regulations by omitting to mention that the presenter of a documentary about the Gaza situation was the child of a Hamas administrator, as ruled by regulatory body Ofcom.
An inquiry by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the programme was "materially misleading".
The BBC's director general had previously apologised, stating there had been "a serious error in relation to accuracy".
The regulator has directed the broadcaster to transmit a peak-time declaration about its decisions.
"Since this amounts to a major infringement of our code, we are directing the broadcaster to broadcast a statement of our determinations against it on the BBC's second channel at 21:00, with a timing to be finalised," the statement read.
The regulator's statement said: "The inquiry we conducted determined that the programme's lack of disclosure that the presenter's parent served in a position in the Hamas-run government was materially misleading.
"It meant that the public did not have essential details which may have been extremely pertinent to their assessment of the voice and the content he presented.
"Credibility is at the core of the relationship between a broadcaster and its viewers, especially for a national broadcasting corporation such as the public broadcaster.
"This failing had the risk to undermine the exceptionally strong amounts of credibility that viewers would have invested in a documentary produced by the BBC about the Israel-Gaza war."
The film was withdrawn from the online platform in February after the boy's family links emerged, and in this past July an corporation's own inquiry found it violated the broadcaster's editorial guidelines on truthfulness.
A corporation official stated: "The authority's determination is in line with the findings of the corporation's inquiry, that there was a serious error in the programme in relation to the broadcaster's journalistic policies on truthfulness, which reflects clause 2.2 of the regulator's media standards.
"We have apologised for this and we agree with Ofcom's decision in its entirety. We will adhere to the penalty as soon as the schedule and wording are confirmed."
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