The public service broadcaster engaged in a "serious breach" of industry standards by omitting to mention that the presenter of a programme about Gaza was the child of a Hamas official, as determined by regulatory body Ofcom.
An probe by the broadcasting watchdog into Gaza: How to Survive a Warzone has concluded that the documentary was "substantially inaccurate".
The chief executive of the broadcaster had previously apologised, saying there had been "a significant failing in relation to factual correctness".
The regulator has instructed the corporation to transmit a peak-time statement about its conclusions.
"Given this constitutes a serious breach of our code, we are ordering the corporation to broadcast a message of our findings against it on BBC Two at 21:00, with a schedule to be determined," it said.
'Potential to Erode Trust'
The authority's statement declared: "Our investigation concluded that the documentary's failure to disclose that the narrator's male guardian held a position in the Hamas-controlled authority was significantly deceptive.
"It meant that the viewers did not have critical information which may have been extremely pertinent to their evaluation of the narrator and the content he provided.
"Confidence is at the center of the relationship between a television network and its viewers, notably for a public service broadcaster such as the public broadcaster.
"This error had the risk to damage the exceptionally strong amounts of credibility that the public would have placed in a BBC factual programme about the conflict in Gaza."
The programme was removed from the online platform in last February after the presenter's family links emerged, and in July an corporation's own inquiry determined it breached the corporation's content policies on truthfulness.
A representative for the broadcaster stated: "The authority's determination is in line with the conclusions of the internal assessment, that there was a major oversight in the programme in relation to the BBC's Editorial Guidelines on accuracy, which reflects Rule 2.2 of the authority's broadcasting regulations.
"We issued an apology for this and we agree with the regulator's ruling in complete. We will comply with the penalty as soon as the schedule and wording are determined."
