“All adults in Denmark can now make an appointment on their own for a COVID-19 test,” the health ministry said in a statement, with a link to a website to make an appointment.
The website is theoretically open to anyone with a NemID, the Danish bank's shared login system.
Until now, only those with symptoms could be tested, once they had received the green light from their doctor.
On Monday, the country registered 41 new cases, the smallest increase since mid-March, bringing the total number to 11,166.
“We've brought the infection rate down to a very low level. It's imperative that there be no hidden pockets of infection that could cause the spread of the virus to increase,” Health Minister Magnus Heunicke said.
The test being offered detects an active case of the virus, and is not an antibody test that determines whether a person has been infected at some point.
After announcing strict measures to curb the virus on March 11, the Scandinavian country was the first in Europe to reopen nursery and primary schools on April 15.
Since then, a number of restrictions have been eased, including the reopening of hair salons, dentists' practices and tattoo parlours, as well as shopping centres and department stores.
On Monday, cafes, bars and restaurants reopened.
The infection rate has since dropped, from 1.0 in late April to 0.7 in the first week of May, health authorities said.
A reproduction rate of 1.0 means that one person with COVID-19 infects on average just one other, while a rate of below 1.0 indicates that the spread is declining.
Denmark has confirmed 548 COVID-19 deaths since the start of the pandemic.