Most dairies will have a roller door which comes down to cover the displays.
The law that introduced the display ban also allows enforcement officers to instantly fine retailers $1000 for selling tobacco to people aged under 18.
It also increases the maximum penalty for selling tobacco to underage people from $2000 to $10,000.
A series of tax rises - with more on the way - has made New Zealand cigarettes among the most expensive in the OECD.
But last week tobacco giant Philip Morris started an aggressive fightback against tobacco regulations, saying they go too far.
The company, which has the third-largest share of the New Zealand tobacco market, is distributing cards to shops directing customers to a website through which smokers can have their say on the regulations.
Retailers are being asked to hand the cards to anyone buying Philip Morris products.
The myopinioncounts.co.nz website was "a place where adult smokers could voice their opinions about regulatory issues'', said Philip Morris spokesman Chris Bishop.
"We talked to our customers ... and we really got the sense that they wanted the ability to learn more about these issues and voice their concerns about them,'' he said.
Anti-smoking groups are aiming to make New Zealand smokefree by 2020.