According to the Health Ministry, the digital certificate was to show if the individual had a negative PCR (Polymerase Chain Reaction) test.
Some countries require such a test to allow entry.
The certificate could also be used to be exempted from quarantine regulations.
It would be available free of charge after undergoing a COVID-19 test in Denmark, and the test results were completed. The test must not be more than seven days to be valid.
However, certificates were to be available for adults over the age of 18 who had a residency in Denmark.
Parents with minors would from mid-July able to download a similar certificate for children.
COVID-19 tests have been available free of charge in Denmark since mid-May.
Earlier, Denmark reviewed the number of people allowed to gather from 50 to 100, amid progress in tackling the pandemic. However, the number increased to 200 as at Aug. 8, under the terms of a parliamentary agreement from June.
Meanwhile, some events, including some matches in the top-flight Danish football league, already allow even higher numbers under special exemptions.
Denmark has gradually re-opened society after shutting its borders and closing down many institutions in March. Schools, restaurants, theatres, cinemas and retail stores had in recent time re-open.
The Scandinavian country had, as of Wednesday, recorded 609 COVID-19 related deaths and about 13,000 confirmed virus cases.