Matti Saari, a 22-year-old student at the school in Kauhajoki, killed nine fellow students and a teacher before shooting himself in the head on September 24.
Both Saari and Pekka-Eric Auvinen, the 18-year-old who carried out the Tuusula shooting, had valid gun licences.
The government said it was also planning to amend laws to give police the authority to perform more thorough background checks on applicants.
The law currently allows people as young as 15 to acquire guns for target or hunting purposes.
Finland has the third-highest level of gun ownership in the world, behind the United States and Yemen, according to a survey carried out last year by the Small Arms Survey of the Graduate Institute of International Studies in Geneva.