Under the new law, smoking will be banned in bars, cafes and restaurants bigger than 100 square metres (1,070 square feet), although separate smoking areas will be allowed. For smaller venues, it will be up to the owner to decide.
It will also be illegal to smoke in workplaces, public buildings, shopping centres, sports halls, cultural centres and other public spaces.
Denmark is the last of the five Nordic countries to introduce a smoking ban.
Danish smokers who flout the law will not be fined but can be asked to leave the premises.
Cafe, bar and restaurant owners who fail to enforce the legislation will however be fined 2,000 kroner (365 dollars, 270 euros) the first time, 5,000 kroner (913 dollars, 672 euros) the second time and 10,000 kroner (1,825 dollars, 1,345 euros) for a third offence.
Employers will be fined 20,000 kroner (3,650 dollars, 2,688 euros).
Opposition to the ban has been vocal in Denmark, in contrast to the relatively warm welcomes similar bans have received in neighbouring Sweden, Finland and Norway.
Numerous petitions have been signed and protest demonstrations have been held in recent months. Demonstrations are planned for Wednesday.
The Scandinavian country had been due to introduce the ban in April but delayed it by four months to give lawmakers more time to consider the legislation.
In Denmark, 25.6 percent of inhabitants over the age of 13 smoke daily, according to a study conducted in December 2005 for public health institutions and cancer and cardiovascular health organisations.
In 2005, 28 percent of the Danish population smoked, or 31 percent of men and 25 percent of women, compared to 41 and 37 percent respectively in 1995, according to statistics.
Smoking bans have already been introduced across Europe, in France, Iceland, Ireland, Italy, Latvia, Lithuania, Malta, Norway, Scotland, Sweden, annd Wales. England introduced a ban on July 1.