He was caught as he tried to flee on a motor scooter.
He was wrestled to the ground and handcuffed before being led away.
He will appear in Auckland District Court tomorrow charged with wounding with intent to cause grievous bodily harm.
Newstalk ZB said the student was a Korean national who had only been at the school for a few weeks.
Police said an associate of the alleged offender was also helping with inquiries.
Mr Warren was taken to Auckland Hospital with serious but not life threatening injuries.
Avondale College principal Brent Lewis told nzherald.co.nz he may be released from hospital tonight.
Mr Lewis told a media conference the stabbing was an isolated incident, and that international students were an important part of the school.
He described the incident as "an aberration, and such a bizarre incident".
All students who witnessed the stabbing had been interviewed by police, and had been offered counselling.
It is understood the Caucasian teacher was taking a Japanese class and was wounded just below the righthand shoulder at about 11.40am.
A scene examination of the classroom is under way.
One reader emailed nzherald.co.nz to say that her daughter was a student at the school and had been locked in the college's squash courts while police searched for the teacher's attacker.
Mr Lewis told nzherald.co.nz students had been asked not to speak to the media but said reports they would be expelled if they did so were untrue.
He said school would continue as normal tomorrow.
An Avondale College student, Manaola Kaumeafaiva, 14, was stabbed to death outside the college in October 2006, after a hip-hop competition organised by a church.
Petani Fa'avae, 16 at the time, was found guilty of murder and jailed for life with a minimum parole period of 11 years.
Prime Minister John Key was today meeting Korean President Lee Myung-Bak in Auckland, and afterwards told NZPA he was shocked by the stabbing.
"This is somewhat alarming ... but we need to understand whether it's an isolated incident out of left field or whether something a bit more serious is going on," he said.
"If it's an isolated incident, we will have to find out the mental state of the student involved.
"I understand he is a foreign student so we will have to look at the implications of that.
"We're literally earning billions of dollars from foreign students who are coming to study in New Zealand."
There were 32,000 law-abiding, honest and trustworthy Koreans living in this country and it was important not to tarnish the reputation of a large group of foreign students who were coming to study in New Zealand, or indeed the Korean people, because of the actions of one person, he said.
"It is possible to get a random individual who is suffering from some sort of mental condition who undertakes an action which is totally reprehensible," Mr Key said.
"There's been issues with foreign students in the past and we've worked hard to try and improve the conditions around them and the partial care that we give those students who come to New Zealand."
- NZHERALD STAFF and NZPA
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