One person, identified as a male Finnish citizen, was taken into custody.
The area has been evacuated, and no further details of what happened have yet been released.
The incident took place at Savo Vocational College, located in a shopping center near the town of Kuopio.
Local news agency STT reported that nine people had been taken to hospital after the incident. "While I was helping the teacher, I started hearing other shouts for help".
One police officer was slightly injured, and the rest of the wounded were students and staff of the school, mostly women aged 15-50.
Police didn't give the suspect's age, but said he was born in 1994 and he's a Finnish national without a prior criminal record.
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One witness told Finnish news site MTV News the attack had been carried out by a student with a sword.
Police have confirmed a violent event at Kuopio Savo vocational school in Herman shopping centre.
Gun laws have since been tightened.
In 2017, two people were killed and eight injured in a stabbing attack in the main square of Turku, a city in southwest Finland.
Finland has seen two deadly school attacks in the past 12 years. The perpetrator, Abderrahman Bouanane, an asylum seeker, was later sentenced to life imprisonment for murder and attempted murder with terrorist intent.