Finnish Student Health Service (FSHS) provides health and medical care, mental health and dental care services for students enrolled at universities in Finland. These services are only available for members of the Student Unions. FSHS is a nationwide organisation with offices in 16 Finnish cities. This service does not, however, provide emergency or hospital care. You should therefore have an insurance that covers such cases.
You can find the contact information, office hours and price lists for the Finnish Student Health Service on their website.