Robert Redeker has been forced into hiding after making controversial remarks about the Prophet Muhammad.
Writing in France's Le Figaro, Mr Redeker described the religion's founder as "a merciless war leader".
Since publishing the article, he has been under police protection and forced to move between safe houses.
On Friday, the Paris prosecutor's office said it had opened a preliminary investigation into the threats to see if they were linked to terrorist activity.
French Prime Minister Dominique de Villepin described the threats as "intolerable".
"We are in a democracy, everyone has the right to express his views freely - of course while respecting others," he said.
Mr Redeker says that his personal details and home address are now available on Islamist websites.
His article was entitled "In the face of Islamist intimidation, what is the world to do?" and was written in reaction to Muslim protests following remarks made by Pope Benedict XVI.
The Pope has since apologised several times and said the views quoted were not his own.
In the article, published on 19 September, the French teacher describes the Koran as a "book of extraordinary violence" and Islam as a religion which "exalts violence and hate".
Mr Redeker says that he fears he will not be able to come out of hiding for the immediate future.
"The Islamists have succeeded in punishing me on French territory as if I were guilty of a speech crime," he said.
Paris-based press watchdog group Reporters Without Borders said the choice not to publish Mr Redeker's article would have represented "a defeat for freedom of thought".
France has one of Europe's largest Muslim communities with an estimated total of six million people, or ten percent of the population.