"Police are carrying out an investigation to identify the author of these unworthy declarations," police said in a statement, adding that the Facebook "wall" page in question had already been taken down.
Following the posting, the French Muslim Council (CFCM) contacted police and the French anti-Islamophobia Collective (CCIF) contacted the social networking site to have the page removed.
The offending statement called on the world to mark the Feast of Sacrifice, known as Eid al-Adha, on November 6 by "cutting Muslim throats instead of sheep".
"We will finally have a good reason to celebrate," it said.
Muslims mark the end of the Hajj pilgrimage to Mecca by sacrificing an animal, often a sheep, in remembrance of Ibrahim's willingness to sacrifice his son for God.
"This is a lamentable call to murder that could bring about a new Oslo," Abdallah Zekri of the CFCM told AFP, referring to July's massacre in Norway carried out by Islamophobe Anders Behring Breivik.
Zekri noted what he said was a rise in Islamophobia in France since President Nicolas Sarkozy's right-wing UMP party started a controversial public debate on French identity, Islam and immigration.
"Today it is easy to attack Muslims with impunity," Zekri said.