The department issued Level 4 travel advisories — the highest level — for both countries, “indicating a very high level of COVID-19 in the country.”
Europe’s return to the pandemic’s epicenter has been blamed on a sluggish vaccine uptake in some nations, the highly contagious Delta variant, and colder weather moving people indoors again.
In Germany, the EU’s most populous nation, just 68 percent of the population is fully jabbed.
The country has urged all vaccinated adults to get a booster jab to combat waning vaccine efficacy after six months.
“Probably by the end of this winter, as is sometimes cynically said, pretty much everyone in Germany will be vaccinated, cured or dead,” German Health Minister Jens Spahn said, as he urged more citizens to get the jab.
Outgoing Chancellor Angela Merkel warned that Germany’s current Covid curbs — including barring the unvaccinated from certain public spaces — “are not enough.”
With intensive care beds swiftly filling up, Germany’s worst-hit regions have ordered new shutdowns, including the closure of Christmas markets.
Denmark meanwhile has a higher vaccination rate at just over 75 percent of the population.
Cases have however been at a high level in recent weeks in the Nordic country, which lifted all coronavirus restrictions in September before reimplementing its Covid-19 health pass earlier this month.