The public service broadcaster committed a "significant breach" of media regulations by omitting to mention that the voice of a documentary about the Gaza conflict was the offspring of a Hamas administrator, as ruled by UK media regulator Ofcom.
An inquiry by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the documentary was "substantially inaccurate".
The head of the BBC had earlier expressed regret, saying there had been "a significant failing in relation to accuracy".
The authority has directed the BBC to air a evening announcement about its decisions.
"Given this constitutes a significant violation of our regulations, we are instructing the BBC to air a statement of our conclusions against it on the BBC's second channel at 9pm, with a timing to be finalised," the statement read.
'Possibility to Undermine Credibility'
The authority's announcement said: "Our investigation determined that the film's omission to reveal that the voice's male guardian occupied a position in the Hamas-run authority was materially misleading.
"This implied that the public did not have critical information which may have been extremely pertinent to their assessment of the narrator and the content he provided.
"Confidence is at the center of the relationship between a broadcaster and its viewers, particularly for a state-funded media outlet such as the public broadcaster.
"This failing had the potential to damage the exceptionally strong degrees of credibility that the public would have placed in a documentary produced by the BBC about the Gaza conflict."
The film was pulled from iPlayer in last February after the presenter's family links emerged, and in the month of July an internal BBC review found it infringed the broadcaster's content policies on truthfulness.
A corporation official commented: "The regulator's decision is in line with the findings of the internal assessment, that there was a serious error in the documentary in relation to the BBC's Editorial Guidelines on truthfulness, which corresponds to regulation 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we comply with the regulator's ruling in its entirety. We will follow the penalty as soon as the timing and wording are confirmed."