The Interior Minister, Manuel Valls, says the incident happened in the city of Limoges sometime between Tuesday night and early Wednesday morning.
“This attack is a grave assault on the dignity of Muslims and is shocking for every citizen who upholds the values of respect and tolerance,” Valls says in a statement.
The attack came a month after two pigs heads were deposited at the entrance of a mosque in Montauban, in the south of France.
It also happened on the same night that protesters attacked the American embassies in Egypt and Libya over a US-made film said to insult the Prophet Mohammed.
The US ambassador to Libya was killed in the attack in the eastern city of Benghazi, but there has been no indication that the desecration at Limoges was linked to the unrest over the film.
In the past, vandals have also sprayed graffiti on the mosque's doors.
France is home to at least four million Muslims, forming the largest Islamic community in Europe.
French Muslim leaders say incidents of Islamaphobia are on the rise against a background of confrontation with the authorities.
Many Muslims have been angered by legislation banning women from wearing full veils in public.
This year's French elections were also marked by debate over the use of halal methods of animal slaughter.