Police say they responded to the incident at Viertola school before 09:00 (06:00 GMT) on Tuesday and urged local residents to remain indoors.
A suspect, who police say was also aged 12, has been arrested.
The school has 800 students and 90 staff. Witnesses told public broadcaster YLE that two ambulances had left the scene.
In common with other Finnish schools, children had just returned to classes in Vantaa, north of the capital Helsinki, after the long Easter weekend.
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Twelve, not 13.
You’re right, there seems to have been some misreporting initially.
Something has gone fundamentally wrong regarding upbringing, school and mental health if a 12-year-old gets access to a gun and starts shooting innocent people as a means of “revenge”.
I think the police have stated they are not yet aware of a possible motive, we know the child’s weapon was registered to a close relative but how they got it and why they used it is still a mystery. Terrible and sad that someone so young felt like taking a life is a valid course of action.
I wonder what will happen to the gun owner. They clearly did not secure their gun.