It would be forbidden to smoke in cinemas, theatres, sport arenas, schools, transport means and roofed platforms and roofed bus and tram stops.
Previous governments have attempted to enact the same restrictions but ran into opposition, leaving the Czech Republic as the last EU member to allow unrestricted smoking in restaurants.
One quarter of Czechs smoke, according to Eurobarometer.
The Health Ministry says the ban includes electric cigarettes and should be applied without exceptions in all indoor spaces of such establishments. The sale of cigarettes in hospitals and schools will also be banned.
Unlike most of Europe, the Czechs have been tolerant to smoking and it is currently up to restaurant owners to decide whether to allow or ban it.
Smokers found breaking the law could be fined up to 5,000 koruna (180 euros, $200) while restaurants could be hit with up to 50,000 koruna.
Twenty-nine percent of Czechs smoke, according to a Eurobarometer poll from 2012. The EU average is 28 percent.
All EU countries have adopted measures to protect citizens against exposure to tobacco smoke but national measures differ considerably in extent and scope.
The bill also includes a provision that requires bars and restaurants to offer at least one non-alcoholic drink on their menu at a price that is cheaper than the cheapest alcoholic drink.
