Police Sgt. Tommi Tikka says the four victims had been taken to the hospital and that their injuries "were not life-threatening."
Tikka said the attacker "likely" was a student at a college in the town of Oulu, 600 kilometers (370 miles) north of the capital, Helsinki, where the stabbings occurred earlier Thursday. No other details were immediately available.
In recent years, Finland has seen two deadly school shootings.
In 2008, a culinary student killed nine fellow students and a teacher before shooting himself at a vocational school in western Finland.
A year earlier, an 18-year-old killed six fellow students, a nurse and the principal at a high school in southern Finland.
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