Fires were set at about 1.00am at five different places in the women's room of a prayer hall in a residential area of Château-Thierry a town of 15,000 residents between Paris and Rheims, sources said on Sunday.
Firefighters intervened before the blaze seriously harmed the building, police told the AFP news agency, but furniture and carpets were damaged and smoke stained the walls both in that room and in the adjoining men's prayer room.
Burnt Korans were found and appeared to have been used to start the fires and other damage, such as blocking sinks with toilet paper, was also inflicted.
'Criminal act' condemned
Interior Minister Bruno Le Roux condemned "intolerable and criminal acts".
There was no doubt that the fires were deliberately caused, according to public prosecutor Jean-Baptiste Bladier.
"The house was in a residential area of the town far from major roads," he said. "You had to know there was a prayer room there because there were no indications that would lead one to assume it."
Deputy mayor Jacques Krabal dubbed the attack a "serious criminal act".
The prayer rooms were run by the town's Moroccan Cultural Association, which has 200 members, he said.