The man, his wife and son were all tested but only the man was diagnosed with the virus, the Danish Health Authority said.
The man, a journalist with broadcaster TV 2, has been isolated in his home together with his family.
“We are of course deeply shocked that what we thought was an unlikely event, is now a reality,” the reporter, Jacob Ramlyng, wrote on Facebook.
Health authorities said the family was doing well and efforts were under way to trace his contacts.
Half of those cases are in the western state of North Rhine Westphalia, where authorities have launched a major initiative to test more people for the virus.
The novel coronavirus causes the Covid-19 lung disease, which can be fatal, although most people who catch the bug experience mild symptoms or none at all.
Edited By: Fatima Sule/Felix Ajide