The fatality “was a person aged 81 years who was hospitalized for other serious illnesses,” said officials at the hospital where the patient was treated.
The death is the fifth COVID-19 fatality in the Nordic countries. Two people have already died in Sweden and two in Norway.
Denmark also became the latest country to take dramatic steps to stop the spread of the COVID-19 disease, closing its borders to all non-resident foreigners for a month.
“All tourists and foreigners who cannot prove that they have a valid reason to come to Denmark will not be allowed to enter,” Prime Minister Mette Frederiksen said Friday when the ban was announced.
Police said that around 20 people were refused entry after the measure came into effect at noon Saturday (1100 GMT).
At Copenhagen airport, passengers said that strict controls were in place for those entering the country.
Only Danes and other permanent residents were let through, as well as others with a “compelling reason” to come into the country.
Trade imports and exports are not affected.
The government on Wednesday unveiled a string of measures to limit the impact of the pandemic, which has now seen more than 150,000 worldwide infected with COVID-19 and caused over 5,000 deaths.
Schools, universities and libraries have been closed in Denmark and civil servants have been asked to stay at home.