The man entered Savo College carrying a sword with which he attacked a woman teacher, injuring her in the head, and stabbed others, including a female student in the stomach, an eyewitness told Finnish media, the BBC reported.
Police said the suspect, who was identified as a Finnish man, was carrying a "bladed weapon" and a gun when he walked into the college, situated in a shopping centre, around midday.
The man walked into a class and attacked the teacher, the Iltahlehti news website reported. As she tried to flee, students threw chairs at the attacker in an attempt to escape even as some were wounded.
"He hit a girl in the neck with a sword and stabbed her in the stomach," an unnamed witness was quoted as saying.
One woman told Finnish TV channel MTV how she had helped the teacher, who suffered a deep wound to her hand, when she was attacked.
Police said its officers used a firearm when detaining the suspect after arriving at the school.
They said a body had been found on the premises, while the assailant and a police officer were among the injured, two of whom are said to be serious.
The college has about 600 students and 40 staff, but officials said it was unclear how many were at the scene at the time of the attack.
It was not clear if the assailant was a student of the college and the police are yet to confirm a motive for the attack.
Prime Minister Antti Rinne said the violence at the college was "shocking and completely unacceptable", while Education Minister Li Andersson said every young person had a right to study in safety, without fear of violence.
Incidents of violence are rare in Finland. In 2008, a 22-year-old gunman shot dead 10 people at a vocational school in the town of Kauhajoki before turning the gun on himself.
( With inputs from IANS )