
The 45-year-old teacher at a school in Aubervilliers, northeast of Paris, was hospitalised with light stab wounds in his side and throat.
He had earlier claimed that a man in overalls and a balaclava had arrived while he was preparing his class on Monday, grabbed a box cutter and scissors that were in the room, and attacked him.
Teacher attacked in Paris suburb by man citing Islamic State: police
The teacher further claimed that the man shouted: "This is Daesh. This is a warning." Daesh is another name for Islamic State.
Prosecutors said they were still questioning the teacher, whose injuries were not considered life-threatening, over why he lied.
With France on edge a month on from attacks in Paris, and with the Islamic State calling for attacks on French schools, the investigation had been immediately taken over by anti-terrorism prosecutors.
The case even prompted a visit by Education Minister Najat Vallaud-Belkacem, who vowed to boost security at France's schools.
The teacher was said to have worked at the school for 20 years, and was "appreciated", according to the town mayor Pascal Beaudet.
He was described by one parent, Nadia Perez, as "very involved in the life of the school."
"He was a personality at the school," she added. "But he could be fairly tough on the kids. He did not tolerate them being impolite."
The Islamic State's French-language magazine Dar-al-Islam called in its November edition for its followers to kill teachers in the French education system, describing them as "enemies of Allah".
"This education, in the case of France in particular, is a means of propaganda used to impose the corrupt way of thought established by the Judeo-masonry," it said.
Islamic State claims responsibility for Paris attacks
"Muslims must know the French education system is built against religion and Islam, as the only religion of truth, cannot cohabit with this fanatic secularism."
Last month's attacks by Islamic State in Paris, that left 130 dead, saw France impose a three-month state of emergency and led to a Europe-wide manhunt for suspects.
"We will continue to reinforce security measures at schools in a context where schools feel threatened," said Vallaud-Belkacem on Monday.
Rachel Schneider of the main primary school teachers' union SNUipp said the Islamic State threats had alarmed members.
Islamic State can make fake Syrian passports: US report
"We have received many calls from colleagues, who are very worried. They don't necessarily think there will be an organised attack, but they fear this message of murderous madness will inspire unstable people to action," she said.
In March 2012militant, Mohamed Merah killed three children and a teacher outside a Jewish school in southwestern France in attacks which also saw him kill three soldiers.
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