The public service broadcaster engaged in a "significant breach" of media regulations by not revealing that the voice of a film about Gaza was the child of a Hamas administrator, as ruled by British broadcasting authority Ofcom.
An inquiry by Ofcom into the documentary titled Gaza: How to Survive a Warzone has found that the programme was "significantly deceptive".
The BBC's director general had already issued an apology, noting there had been "a major oversight in relation to accuracy".
Ofcom has instructed the broadcaster to broadcast a peak-time announcement about its findings.
"As this represents a significant violation of our regulations, we are instructing the broadcaster to transmit a message of our conclusions against it on BBC2 at 9pm, with a timing to be confirmed," it said.
'Potential to Damage Trust'
The watchdog's announcement said: "Our investigation found that the film's omission to reveal that the narrator's father served in a position in the Hamas-run government was substantially inaccurate.
"It meant that the public did not have essential details which may have been very significant to their evaluation of the narrator and the details he provided.
"Credibility is at the center of the relationship between a television network and its public, particularly for a state-funded media outlet such as the British Broadcasting Corporation.
"This error had the risk to damage the very considerable degrees of credibility that viewers would have invested in a BBC factual programme about the conflict in Gaza."
The documentary was removed from iPlayer in last February after the presenter's family links came to light, and in the month of July an internal BBC review concluded it breached the corporation's journalistic standards on factual correctness.
A BBC spokesperson commented: "The regulator's decision is in agreement with the results of Peter Johnston's review, that there was a serious error in the film in relation to the broadcaster's journalistic policies on factual correctness, which reflects clause 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we agree with the regulator's ruling in complete. We will follow the directive as soon as the date and language are finalised."