Guler senior was described as head of the Islamic Association in France which runs the mosque in Paris's Bastille area, although he does not preach.
The interior ministry confirmed that Guler faced possible expulsion but gave no further details.
His arrest came on the day that French Interior Minister Dominique de Villepin pledged to press ahead with the deportation of radical Muslim clerics, while keeping in close touch with leaders of the country's large Muslim community on the issue.
Last month the Government experienced an embarrassing setback when a court ruled illegal its decision to expel to his native Algeria a radical fundamentalist imam from the south-eastern city of Lyon after he justified 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," Mr 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-fundamentalist Kaplanci movement, which calls for an Islamic state in Turkey, said Haydar Demiryuek, spokesman for the French Council of the Muslim Faith (CFCM).
Kaplanci is banned in Germany, he said, adding that of France's 400,000 Turkish residents no more than 500 adhered to the fundamentalist group.