The public service broadcaster was found to have committed a "major breach" of broadcasting rules by not revealing that the voice of a programme about Gaza was the offspring of a Hamas official, as determined by regulatory body Ofcom.
An investigation by the broadcasting watchdog into the programme Gaza: How to Survive a Warzone has determined that the film was "significantly deceptive".
The chief executive of the broadcaster had already issued an apology, stating there had been "a significant failing in relation to factual correctness".
The authority has instructed the broadcaster to transmit a evening statement about its decisions.
"As this represents a significant violation of our regulations, we are directing the corporation to broadcast a announcement of our determinations against it on BBC Two at 21:00, with a date to be finalised," the statement read.
'Possibility to Undermine Trust'
The regulator's report said: "Our probe concluded that the film's failure to disclose that the narrator's male guardian held a post in the Hamas-administered administration was significantly deceptive.
"It meant that the audience did not have vital facts which may have been very significant to their assessment of the voice and the content he presented.
"Confidence is at the core of the bond between a television network and its audience, particularly for a public service broadcaster such as the BBC.
"This oversight had the possibility to erode the exceptionally strong levels of confidence that the public would have placed in a documentary produced by the BBC about the conflict in Gaza."
The documentary was removed from iPlayer in February after the presenter's family links came to light, and in July an internal BBC review found it infringed the broadcaster's journalistic standards on factual correctness.
A BBC spokesperson commented: "The Ofcom ruling is in accordance with the findings of Peter Johnston's review, that there was a major oversight in the documentary in relation to the BBC's Editorial Guidelines on factual correctness, which corresponds to Rule 2.2 of Ofcom's Broadcasting Code.
"We have apologised for this and we accept the authority's determination in its entirety. We will follow the penalty as soon as the schedule and wording are finalised."
