The conscript disappeared during an orienteering exercise in Kouvola. He was armed with an assault rifle and a small number of cartridges.
The Finnish Defence Forces had been searching for him since Monday afternoon.
On Tuesday a helicopter and teams of police with dogs joined the effort, which was extended over a larger area.
The man went missing from the Ahvenlampi training area near the Karelia Brigade's Vekaranjärvi military base. All buildings in the area have been searched.
The man began his compulsory military service in July, and had not had any previous infractions.
His family has been informed and the Brigade is arranging crisis counselling for his fellow conscripts. Kouvola police have begun an investigation into the cause of his death.