Well, not for public bodies at least: “ Administrative fines cannot be imposed on public organisations, such as the government or state-owned companies, municipalities and parishes” [1]
But luckily this sort of thing never happens in the public sector. Except for when it does: https://yle.fi/a/74-20094950
That's interesting, because if you go here https://www.enforcementtracker.com/ there are a lot of public institutions being hit with fines (if they are enforced it's another issue) - search for Municipality for example
However I don't see any municipality in Finland getting fines