The British broadcaster was found to have committed a "significant breach" of media regulations by failing to disclose that the narrator of a programme about Gaza was the offspring of a Hamas representative, according to British broadcasting authority Ofcom.
An inquiry by Ofcom into Gaza: How to Survive a Warzone has concluded that the programme was "substantially inaccurate".
The chief executive of the broadcaster had earlier expressed regret, saying there had been "a major oversight in relation to truthfulness".
The authority has ordered the BBC to air a evening declaration about its decisions.
"As this represents a major infringement of our regulations, we are instructing the BBC to broadcast a message of our conclusions against it on BBC Two at 21:00, with a timing to be finalised," it said.
'Possibility to Erode Trust'
The regulator's statement stated: "Our investigation determined that the film's lack of disclosure that the voice's male guardian held a role in the Hamas-administered authority was significantly deceptive.
"It meant that the viewers did not have essential details which may have been extremely pertinent to their evaluation of the voice and the content he provided.
"Trust is at the core of the connection between a broadcaster and its public, notably for a national broadcasting corporation such as the public broadcaster.
"This error had the possibility to damage the exceptionally strong amounts of confidence that audiences would have put in a BBC factual programme about the Gaza conflict."
The programme was pulled from iPlayer in February after the presenter's family links came to light, and in this past July an internal BBC review concluded it infringed the broadcaster's journalistic standards on factual correctness.
A representative for the broadcaster said: "The Ofcom ruling is in accordance with the results of Peter Johnston's review, that there was a significant failing in the film in relation to the broadcaster's journalistic policies on truthfulness, which reflects Rule 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we accept the regulator's ruling in full. We will adhere to the sanction as soon as the timing and language are determined."