Eight apparent victims of the attacker were also found and sent to local hospitals.
Another ten people were injured, two of them seriously, before armed police arrested one person at the scene.
The shopping centre, which is a few kilometres outside the center of Kuopio, houses the Savo Vocational College, where the attacker allegedly entered with some sort of sword, according to Finnish media.
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Police officers discharged a firearm in apprehending the attacker. Police have detained one perpetrator.
She also told Finnish news agency STT that students described the weapon as "a long sword", and that he "started swinging the sword around in the class". "The injured have been evacuated", East Finland police said in a statement.
Finland's prime minister, Antti Rinne, tweeted that the violence was "shocking and completely unacceptable". The suspect and another person were said to be "severely" injured.
Finland has seen two deadly school attacks in the past 12 years. In 2008, a 22-year-old gunman shot dead 10 people in the town of Kauhajoki before fatally shooting himself.