The proposal has been put forward by a working group at the Finnish Ministry of Social Affairs and Health.
The goal is a Finland free of tobacco and nicotine products by 2030, writes Svenska Yle.
If the proposal becomes law, Finns will have had to turn 20 to be allowed to buy, import or own tobacco products, instead of 18 as today.
There will also be an end to smoking both at outdoor restaurants and at home - for those who live in apartment buildings - and a stop to all snus imports into the country.
Increasingly popular - despite the ban
Today, 12 percent of Finland's adult population smokes daily.
Around 5,000 Finns die each year as a result of smoking, according to official figures.
Snus was banned in Finland when the country joined the EU in 1995, but has become increasingly popular in recent years.
Most of the snus is brought into Finland from Sweden.