The display of such goods has been illegal in large stores and supermarkets since 2012.
Now small stores, and other outlets such as pubs and clubs, will also have to keep cigarettes out of sight.
The ban has been welcomed by campaign group Action on Smoking and Health (ASH), but criticised by shopkeeper group the Tobacco Retailers' Alliance.
Hazel Cheeseman, director of policy at ASH, said: "Two-thirds of smokers start before the age of 18, so it is vital that everything is done to put tobacco out of sight to protect future generations.
But Suleman Khonat, spokesman for the Tobacco Retailers' Alliance, said "The introduction of the display ban into larger shops hasn't even been evaluated, so how do we know it will work in smaller shops? Of course retailers will need to comply with the law but this is a further unnecessary measure that will hit small businesses".
