The attack, reported yesterday by the teacher, set off a manhunt in the northern suburb of Aubervilliers.
Both the Paris prosecutor’s office and the local prosecutor said the teacher was being questioned.
They added that the story about the attack had been based on his testimony.
The false report comes as France remains under a state of emergency after the November 13 attacks in Paris by IS-linked extremists that left 130 people dead and hundreds wounded.
A few weeks later, IS urged its followers to attack teachers in France, saying the secular education system was poisoning young minds.
Aubervilliers, a northern suburb, is only 4km from the apartment where the suspected organiser of the November attacks was killed in a police raid.
French schools have imposed strict security measures since previous attacks in January, with doors locked during the day, identity checks for visitors and periodic bag searches.
Families dropping off or picking up children are not permitted to linger near schools’ entrances, and children are not allowed to wait outside for the doors to open.
The teacher had told police a hooded man claiming to be acting for IS attacked him with a boxcutter as he prepared for classes in a school north of Paris.
The teacher was taken to hospital after the ‘attack’.
The teacher told police the assailant slashed at his neck and said the act was a signal from IS, also referred to in France by the name Daesh.
“This is Daesh, it’s a warning,” he said the attacker told him.