The victims were taken to hospital on Tuesday, a police spokesperson told Reuters.
No further details were immediately available.
The shooting took place at the Viertola school in Vantaa, a suburb of the capital Helsinki, which has around 800 pupils and a staff of 90 people, according to the local municipality.
"The immediate danger is over," the Viertola school's principal Sari Laasila told Reuters, declining to comment further on the incident.
"The day started in a horrifying way. There has been a shooting incident at the Viertola school in Vantaa. I can only imagine the pain and worry that many families are experiencing at the moment. The suspected perpetrator has been caught," Interior Minister Mari Rantanen said on social media platform X.
Previous school shootings in Finland have put a harsh focus on Finland's gun policy.
In 2007, Pekka-Eric Auvinen shot and killed six students, the school nurse, the principal, and himself using a handgun at Jokela High School, near Helsinki.
A year later, in 2008, Matti Saari, another student, opened fire at a vocational school in Kauhajoki, located in northwest Finland. He killed nine students and one male staff member before turning the gun on himself.
Finland tightened its gun legislation in 2010, introducing an aptitude test for all firearms licence applicants. The age limit for applicants was also changed to 20 from 18.
There are more than 1.5 million licensed firearms and about 430,000 licence holders in the nation of 5.6 million people, where hunting and target shooting are popular activities.
