The attack at the Viertola school near Helsinki on Tuesday, in which two other children were also severely injured, was believed to have been triggered by bullying, investigators have said.
"The preliminary investigation has found evidence that indicates the act was planned," police said in a statement, citing unspecified materials found on a phone and computer.
The boy, apprehended by police some 4 km (2.5 miles) from the school, is too young to be tried in court and is now in the care of social services. Police say he has admitted the attack.
After school shootings in 2007 and 2008 in which 20 people died, Finland tightened gun laws in 2010, introducing an aptitude test for licence applicants and raising the minimum age 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.
Police said they have a preliminary understanding of how the 12-year-old suspect obtained the gun, which belonged to a close relative, but investigations were still underway.
The probe into the shooting was expected to take months.
"What happened deeply touches the whole of Finland," the government said in a statement after it was briefed on Thursday on the investigation. "The background and reasons for the incident will be examined thoroughly and necessary measures will be assessed later."
Investigators said they may be able to interview one of the two hospitalised children in the next few days.
(Reporting by Essi Lehto, writing by Anna Ringstrom, editing by Terje Solsvik, Andrew Cawthorne and Christina Fincher)
