According to the latest figures from SSI, the country's infectious disease agency, Denmark registered 3,486 new infections between September 1st and September 15th, bringing its weekly average to 30.02 infections per 100,000 citizens.
Danish authorities ban tourists from countries where the number of new cases of infection per 100,000 exceeds 30 per week, and Danish residents are advised against travelling to them.
The Norwegian Institute of Public Health has already advised its government to put the last open regions of Denmark on its red list, meaning the entire country is likely to be off limits from Saturday.
According to the UK's Daily Telegraph, Denmark could be removed from the UK's quarantine-free travel list later today.
At the same time, the Copenhagen capital region is now above the German travel threshold of 50 new infections per 100,000.
“It's a huge challenge. We must really hope that we get a handle on the infection in Denmark,” Anders Rosbo, head of communications at the tourist organisation Visit Denmark, told state broadcaster DR.
“If [the infection rate] develops so much that even Germany advises its citizens not to come up here, then it will be a major disaster.”
German citizens accounted for a full third of the tourists visiting Copenhagen in July.
Rosbo said that the agency had already stopped a marketing campaign in Norway and expected it would also have to pull the autumn campaign it had planned to launch in The Netherlands.