The British broadcaster committed a "major breach" of industry standards by not revealing that the voice of a programme about the Gaza conflict was the son of a Hamas administrator, as determined by regulatory body Ofcom.
An investigation by the media regulator into Gaza: How to Survive a Warzone has determined that the documentary was "substantially inaccurate".
The BBC's director general had earlier expressed regret, saying there had been "a major oversight in relation to accuracy".
Ofcom has directed the corporation to air a evening statement about its findings.
"Since this amounts to a serious breach of our rules, we are directing the broadcaster to broadcast a statement of our findings against it on the BBC's second channel at 21:00, with a date to be confirmed," the statement read.
'Potential to Undermine Confidence'
The authority's announcement stated: "Our investigation found that the programme's omission to reveal that the narrator's father held a role in the Hamas-administered administration was substantially inaccurate.
"It meant that the viewers did not have essential details which may have been extremely pertinent to their assessment of the narrator and the information he provided.
"Credibility is at the core of the connection between a television network and its public, particularly for a public service broadcaster such as the public broadcaster.
"This oversight had the possibility to undermine the significantly high levels of credibility that audiences would have put in a factual film from the broadcaster about the Gaza conflict."
The film was removed from the online platform in last February after the presenter's family links came to light, and in this past July an corporation's own inquiry found it violated the corporation's content policies on accuracy.
A representative for the broadcaster stated: "The regulator's decision is in agreement with the results of Peter Johnston's review, that there was a significant failing in the documentary in relation to the corporation's content standards on truthfulness, which aligns with clause 2.2 of Ofcom's Broadcasting Code.
"We expressed regret for this and we comply with the regulator's ruling in its entirety. We will comply with the penalty as soon as the schedule and language are finalised."