The US hosting service, Network Solutions, said it was investigating complaints that it may have breached guidelines on hate language.
Dutch politician Geert Wilders says the 15-minute film describes Islam as “the enemy of freedom”.
The planned release has sparked angry protests in many Muslim countries.
The Dutch government has disassociated itself from Mr Wilders’ views, but there are fears the film will spark protests similar to those that followed the publication in Denmark two years ago of cartoons seen as offensive to Muslims.
The film has already been condemned by several Muslim countries, including Iran and Pakistan.
Mr Wilders’ film is entitled Fitna, an Arabic word used to describe strife or discord, usually religious.
Mr Wilders wrote a commentary in a Dutch newspaper on Saturday.
“The film is not so much about Muslims as about the Koran and Islam. The Islamic ideology has as its utmost goal the destruction of what is most dear to us, our freedom,” he wrote in De Volkskrant.
“Fitna is the last warning for the West. The fight for freedom has only just begun,” he said.
He had been using Network Solutions to promote the film.
But on Sunday, Network Solutions said it had received a number of complaints that were under investigation.
It said the site was suspended until it was established whether the content of the site violated Network Solutions’ terms of acceptable use.
They include “material that is obscene, defamatory, libellous, unlawful, harassing, abusive… hate propaganda” and “profane, indecent or otherwise objectionable material of any kind or nature”.
Mr Wilders has had police protection since Dutch director Theo van Gogh was killed by a radical Islamist in 2004.
€¢ Original title: Dutch Islam film website ‘shut’