Islam: The Untold Story has led to more than 1,000 complaints being submitted to Channel 4 and media regulator Ofcom since it was broadcast two weeks ago.
The presenter, the historian Tom Holland, has also been subjected to abuse on Twitter for the programme, which claimed that there was little written evidence supporting the origin of the religion.
Inayat Bunglawala, the media secretary of the Muslim Council of Britain, accused Holland of "bizarre conjecture about Islam's birthplace".
Channel 4 has now opted to cancel a small, post-transmission screening of Islam: The Untold Story for people involved in the programme and other interested parties at its headquarters in London.
In a statement yesterday (September 11), a Channel 4 spokesperson said: "Having taken security advice we have reluctantly cancelled a planned screening of the programme, Islam: The Untold Story.
"We remain extremely proud of the film, which is still available to view on 4oD."
Islam: The Untold Story has also been shown again on 4Seven, Channel 4's new catch-up television channel.
The Guardian reports that Channel 4 opted to cancel the screening after taking advice from "relevant security authorities".
Dr Jenny Taylor, an academic who had been invited to the screening, said that it was "appalling" that the event had been cancelled.
She said that media coverage was a factor in creating "a false storm of protest" around the programme.
"We have got to be able to discuss history. That is the Western way. That is what we do here," she told The Guardian.
"Every other civilisation that Tim has written about has come in for the same treatment. Why should Islam be left out?"
He also noted that his programme was in keeping with other Channel 4 programmes about the historical context of world religions, such as The Bible: A History.
"As a non-Muslim historian I tried to examine, within a historical framework, the rise of a new civilisation and empire that arose in the late antique world as the two great ancient empires of Rome and Persia were in decline," said Holland in a post on the Channel 4 website.
"The themes in the programme have been previously written about extensively by many other historians including: Patricia Crone, Professor at Princeton; Gerald Hawting, Professor at SOAS; and Fred Donner, Professor at Chicago all of whom lent their support to the programme. The themes it explores are currently the focus of intense and escalating academic debate.
"An accusation laid against the film is one of bias and, although I believe that absolute objectivity is a chimera, what was incumbent upon us, in making the film, was to be up-front about my own ideological background and presumptions, and to acknowledge the very different perspective that Muslim faith provides.
"If the film was about the origins of Islam, then it was also about the tensions between two differing world-views. Whether one accepts or rejects the truth of the tradition is ultimately dependent upon the philosophical presumptions that one brings to the analysis of the sources."