Kasem Said Ahmad, chairman of the Danish Islamic Burial Foundation, said: "We are pleased, happy. It is an expression that Islam and Muslims are a part of Danish society."
The Ministry of Ecclesiastical Affairs approved construction of the burial site on 50,000 sq m (540,000 sq ft) of land the foundation bought in southern Copenhagen several years ago.
Denmark's centre-right government under Anders Fogh Rasmussen, the prime minister, has been accused of religious intolerance, partly because of a crackdown on immigration. One of the main areas of contention with the Muslim community has been the lack of a Muslim cemetery.
Local politicians had opposed the development.
More than 50 people were killed earlier this year in protests in Asia, Africa and the Middle East after Danish daily newspaper Jyllands-Posten, and later other Western media, published 12 cartoons about Prophet Muhammad in September.
Three Danish embassies were attacked and many Muslims have boycotted Danish goods due to the row. Muslims consider images of prophets disrespectful and caricatures blasphemous.
"Against the unfortunate background of the publishing of the cartoons, I see this as an expression of accommodation and tolerance that I believe, fundamentally, characterises the Danish government - also in regard to Muslims," said Ahmad.
At present, the dead are either returned to their country of origin for burial, or interred in the Muslim sections which exist in up to 10 public cemeteries in the country.
More than 80% of Danes are members of the state Lutheran church. There are about 200,000 Muslims in Denmark, roughly three per cent of the population.