The 82-year-old head of state, who has been on the throne for half a century, has cancelled her appointments for the week.
Queen Margrethe, who has been vaccinated against the coronavirus, was also diagnosed with Covid-19 in February this year, showing mild symptoms at the time.
Her half-century reign now makes her Europe’s longest-serving monarch following the death of Elizabeth II, 96, who ruled for 70 years, on 8 September. Out of respect for the late British monarch, Margrethe had asked her court to adjust the programme for her own 50-year anniversary commemorations earlier this month.
Among the events she cancelled at short notice was appearing on the Amalienborg Palace balcony to greet well-wishers and a ride in a horse-drawn carriage through Copenhagen. Margrethe was proclaimed queen in January 1972, a day after her father, King Frederik IX, died following a short illness.
The funeral of Queen Elizabeth took place on Monday amid great pageantry. Queen Margrethe was among the hundreds of world leaders, current and ex-monarchs who attended the event.
Other monarchs in London on Monday included those from the Gulf, while the US president Joe Biden and France’s Emmanuel Macron were among the highest-profile political leaders.
The event was watched widely across Britain and the world, with the BBC claiming a high of 28 million people watched its coverage.
Meanwhile, live footage of the Queen lying-in-state was streamed 25 million times across BBC online, it said.