Correspondents say this is the government’s biggest attempt so far to change Cuban smoking habits.
The ban extends to theatres, buses, taxis, trains, schools, food preparation areas and sports arenas.
Smoking will be restricted in restaurants, but it is not clear whether any restrictions will apply in bars.
Tobacco products, the sale of which is currently unrestricted, will be banned for children under 16. Shops closer than 100m to schools will be unable to sell the products.
Cigarette vending machines are also apparently set to become obsolete.
Partial or total smoking bans are already in force in several European countries, in the US state of California and in New York city. Several other countries are considering bans.