His victim is said to have previously shown cartoons of the Prophet Muhammad to his pupils during a discussion about freedom of expression.
This morning, authorities in Paris confirmed that the attacker was an 18-year-old Moscow-born man from Chechnya.
The attacker confronted the teacher in the street near a school in a district of north-western the city called Conflans-Sainte-Honorine at around 5pm (3pm GMT), using a long knife to cut off his head.
Eyewitnesses said they heard the attacker shout "Allahu Akbar", which means "God is Greatest", according to Reuters news agency.
The attacker then fled the scene, but was confronted by police in the nearby district of Éragny.
After a standoff with police, in which they claim he threatened them, officers shot and killed him.
It is understood that nine people, including a minor, have been arrested in connection with the incident.
Speaking to reporters at the scene last night, French President Emmanuel Macron called the incident an “Islamist terrorist attack”, vowing: “They won’t win...we will act.”
Mr Macron said the as-yet unnamed teacher, who is thought to have taught History and Geography, was murdered because he “taught freedom of expression”.
Fourteen people are currently on trial in France for their alleged roles in the terrorist attack on the officers of the satirical magazine, Charlie Hebdo, in 2015.
They are accused of helping two militant Islamist attackers, who shot dead 12 people at magazine’s Paris office in January 2015.
In a later attack, a third gunman murdered a policewoman, then attacked a Jewish grocery shop, killing four people.
According to France’s Le Monde newspaper, the teacher asked Muslim students to leave the classroom if they thought they would be offended by cartoons of the Prophet Muhammad during a discussion on the Charlie Hebdo trial.
He then reportedly showed the class the cartoons, published in the magazine in 2006, which caused outrage among some Muslims.
The French media reports that earlier this month, some Muslim parents complained to the school about the teacher’s decision to show the cartoons.