The country is following a growing trend across Europe and the world of bans on smoking in public places.
Pro-smoking lobbyists say the ban will lead to a drop in business, but others say any losses will be made up by non-smokers going out more.
Patrons of cannabis cafes will still be allowed to smoke marijuana as long as it is not mixed with tobacco.
Possession of cannabis is illegal in the Netherlands, but holders of small amounts are not prosecuted. Smoking cannabis is permitted in licensed cafes.
A Rotterdam cinema handed out free cigarettes on Monday night, hours before the ban came into force on Tuesday.
One hospitality industry forecast said there has been an increase in the number of businesses up for sale ahead of the ban, as owners anticipated slower business because of smokers staying away from restaurants, cafes and bars.
But other studies suggested that their numbers would be replaced by non-smokers going out more to enjoy a night out in a cleaner environment.
Any businesses caught allowing customers to smoke would be warned and repeat offenders would face escalating fines, Chris Krikken, a spokesman for the Food and Wares Authority charged with enforcing the ban, told the Associated Press.