Earlier there was a specific law about edged weapons, however that was replaced in 2003 with Public Order Law (my translation, originally Järjestyslaki).
Text is mostly clear: possession of edged weapons, capable of being used to slash or stab and other items that can be used for harming others is prohibited in public places, unless they are needed for work or there is some other acceptable reason. "Public place" means street, sidewalk, park, marketplace, sports ground, buildings, offices, public transport, restaurant etc.
So in short: no knives in urban and populated areas. Legally, it doesn't matter what type or what blade length even though many people are under the impression that there is a mention of acceptable blade length.
Penalty for possession is normally a fine and confiscation of item.