The man, Mihdat Guler, is a 45-year-old Turkish national who has lived in France for 28 years, according to his son Abdurraham Guler.
Guler senior was described as the head of the Islamic Association in France, which runs the mosque in Paris' Bastille area, although he does not preach.
The Interior Ministry confirmed that Guler faced possible expulsion.
"Midhat Guler is the leader in France of an extremist Turkish Islamic movement which advocates resorting to violence and terrorism," the ministry said in a statement.
His arrest late on Saturday came on the day that French Interior Minister Dominique de Villepin pledged to press ahead with the deportation of Muslim clerics the country views as extreme.
Last month the government experienced an embarrassing setback when a court ruled illegal its decision to expel to his native Algeria an imam from the south-eastern city of Lyon after he was accused of justifying wife-beating in a magazine article.
The imam has since applied for a visa to return to France.
"A hard line against those who advocate violence is the best guarantee of a peaceful practice of the Muslim religion," de Villepin told a private meeting of regional Muslim religious leaders at the Paris headquarters of the Federation of Turkish Muslims.
Guler's mosque comes under the international umbrella of the ultra-conservative Kaplanci movement, which calls for an Islamist state in Turkey, said Haydar Demiryuek, spokesman for the French Council of the Muslim Faith (CFCM).
De Villepin wants to forge ahead
with expulsion of Muslim clerics
Kaplanci is banned in Germany, he said, adding that of France's 400,000 Turkish residents, no more than 500 adhered to the outfit.
Guler's son, Abd al-Rahman, said his father, who had been in France for 28 years, did not understand why he had been held.
"I've seen him. He doesn't understand," Abd al-Rahman told reporters. "Of course I'm worried. It's unacceptable."
Guler took care of the administration of the mosque in the 11th arrondisement of Paris but did not preach, his son said.
"He's just the person in charge of the mosque and nothing more," Abd al-Rahman said. "My father has presided over this mosque since 1984, there have never been problems, not an anti-Semitic word or anything, never."