The rally, set for Saturday in the Swiss capital, follows similar protests in Paris, London and other European cities.
The Central Islamic Council (CCIS), one of the groups involved, said it condemned what it called the “latest provocation” posed by the amateur video.
Entitled “Innocence of Muslims”, the film backed by anti-Islam groups in America is a low-budget production that received little attention when it was advertised on YouTube in July.
But after Egyptian television showed parts of the film, protests erupted in more than half a dozen countries, including Egypt, Yemen, Tunisia and Morocco.
In a statement, the CCIS condemned the film for “denigrating Islam” and “insulting the prophet Muhammad in an absolutely primitive manner”.
It said that “this sort of deliberate violation of religious views” should not be protected by freedom of expression laws.
The council has urged the US government to take action against what it called an “unjustifiable” provocation.
Nicolas Blancho, chairman of the CCIS, said he was not part of the organizing committee for Saturday’s rally.
“But I find it is for a good cause,” he told Le Matin.ch.
Blancho, a Swiss who converted to Islam, said he did not support the violent protests that have led to deaths and injuries in other countries.
“That was a bad way to express anger,” he said.
“The CCIS has always condemned violence. But we must understand that this sort of Islamophobic propaganda (referring to the US video) is about the religious views of Muslims.”
Blancho criticized the American government for not blocking the video, noting that if it had been an film denying the Holocaust, the response would have been “much more strict”.
Not all Muslim groups in Switzerland are supporting the planned rally, with two organizations distancing themselves from the protest.
“We need dialogue not demonstrations," Farhad Afshar, Iranian chairman of a group coordinating Islamic organizations in Switzerland, told Le Matin.ch.