The teacher, a 55-year-old woman, was alone in a classroom at the vocational college in Ibbenbüren, North Rhine-Westphalia, when the knife attack happened, according to police in the city of Münster.
The student called emergency services and did not resist arrest, police said.
There was a large police presence at the college as inquiries got underway. A rescue helicopter, ambulance and an emergency chaplain were also at the scene.
Münster police are carrying out an investigation.