He was holding a licensed handgun owned by a close relative and admitted carrying out the shooting in an initial interview, they added.
The shooting took place on Tuesday morning at the Viertola school in Vantaa, a suburb of the capital, Helsinki.
Police said they were made aware of the shooting shortly after 9am local time, after which they warned bystanders to stay indoors and away from the area and not to open their doors to strangers.
The Finnish broadcaster Yle reported that parents at the school said the suspected shooter was a sixth-grade student there.
Previous school shootings in Finland have put a harsh focus on the country’s gun policy.
There are more than 1.5m licensed firearms and about 430,000 licence holders in the nation of 5.6 million people, where hunting and target shooting are popular activities.
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