I have no idea whether there is legislation to prevent STRs in Finland you would need to check with your local government. @Lucas561
However, I would have thought that if you rent a property from him, that what he is referring to is that you are probably breaking the terms of your lease to sub-let as a short term rental.
I am a landlord as well as someone who hosts on Airbnb. If you broke the terms of the lease by sub-letting the long term rental property I own, I would evict you. (again not sure how tenancy agreements work in Finland).
Have you checked your lease? Did you ask the landlord what he meant when he said it was illegal?
If you are sub-letting your lease contrary to the terms on your tenancy you will need to stop immediately, notify Airbnb and pay any fines for upcoming booking cancellations. Hopefully if you are apologetic and assure the landlord that you will stop immediately, he will not take legal action against you.