Among those detained are four relatives of the suspect, including a minor, who were arrested immediately after the attack.
French police arrested nine people after a suspect beheaded a school teacher in broad daylight on Friday in the street in a Paris suburb.
Samuel Paty, who recently showed cartoons of the Prophet Muhammad to students, was beheaded outside his school.
The police shot the attacker minutes after he murdered the 47-year-old history teacher.
Paty had shown his students caricatures of the Prophet on freedom of expression in a citizenship class earlier this month and angered a number of Muslim parents.
Muslims believe that any portrayal of the Prophet is blasphemous.
The murder was described on Friday by French President Emmanuel Macron as a “terrorist attack”.
Prime Minister Jean Castex said: “I want to share with you my utter indignation. Secularism, the backbone of the French Republic, was targeted in this hideous act. “
Immediately after the attack in the middle-class suburb of Conflans-Sainte-Honorine, four relatives of the attacker were arrested, including a minor. Five others were detained overnight, including two parents of students from the College du Bois d’Aulne, where the teacher was employed.
Parents of students put flowers at the school gate. Some said their children were upset.
“[My daughter] is in pieces, terrorized by the violence of such an act. How will I explain the unthinkable to her? “A father wrote on Twitter.
Muslim leaders condemned the killing, which many public figures perceived as an attack on the very essence of French statehood and its values of secularism, freedom of religion and freedom of expression.
Tareq Oubrou, the imam of a Bordeaux mosque, said of killing: “It is not a civilization that kills an innocent person, it is barbarism.”
“We thank you every day that goes by without incident,” he said. “We’re between hammer and anvil. It attacks the republic, society, peace and the essence of religion, which is about togetherness. “
France has seen a number of violent attacks in recent years, including bombings and shootings in November 2015 at the Bataclan Theater and locations around Paris, in which 130 people were killed.
Late last month, a man who had emigrated to France from Pakistan attacked and wounded two people with a meat cleaver outside the former offices of the satirical magazine Charlie Hebdo.
This was the place where gunmen shot dead employees of the magazine five years ago in retaliation for the magazine’s publication of cartoons of the Prophet.
The edition of the cartoons was revived last month when Charlie Hebdo decided to republish it to coincide with the start of the trial of accomplices in the 2015 attack.