Sweden's King Carl XVI Gustaf and Queen Silvia were among those in the country to test positive for the coronavirus, the palace said in a statement on Tuesday.
Sweden set a new daily record for infections, the most recent data from the health agency showed on Tuesday, registering 11,507 cases on December 30.
"The King and Queen, who are fully vaccinated with three injections, have mild symptoms and are feeling well, given the circumstances," the palace said in a statement.
The palace said the king, 75, and the queen, 78, were self-isolating and that work to trace those they had been in contact with was underway.
After a calm autumn, Sweden has noted a surge in infection in recent weeks.
In the four-day period from Friday through Monday, the country registered 42,969 new cases and 20 deaths, the Public Health Agency figures showed.
Greece reported a record 50,126 coronavirus infections on Tuesday, breaking a previous high of 40,560 registered on December 31.
As recently as December 27, only 9284 new infections were recorded in a day.
The number of deaths recorded in a day dropped to 61 from 78 on Monday.
The country imposed new curbs on bars, restaurants and nightclubs last week following the surge of infections with the Omicron variant over the Christmas holidays.
Hundreds of thousands of students and teachers will nonetheless return to class as scheduled on January 10 but pupils will need to be tested three times during the first week - once more than before the holidays.
"Nothing can replace in-person schooling," Education Minister Niki Kerameus said in a televised briefing.
The United States reported almost one million new coronavirus cases on Monday, according to a Reuters tally, a global record nearly double the country's peak of 505,109 set just a week ago.
The number of hospitalised COVID-19 patients has risen nearly 50 per cent in the last week and now exceeds 100,000, a Reuters analysis showed, the first time that threshold has been reached since the winter surge a year ago.
Overall, the US has reported a daily average of 486,000 cases over the last week, a rate that has doubled in seven days and far outstrips that of any other country.
The record of 978,856 new infections on Monday includes some cases from Saturday and Sunday, when many of the country's states do not report.
The average number of deaths per day has remained fairly steady throughout December and into early January at about 1300, according to a Reuters tally, though deaths typically lag behind cases and hospitalisations.
Omicron is appears to be far more easily transmitted than previous iterations of the virus although the World Health Organisation said on Tuesday that evidence thus far suggests the variant is causing less severe illness.
Nevertheless, US public health officials have warned that the sheer volume of Omicron cases threatens to overwhelm hospitals, some of which are already struggling to handle a wave of COVID-19 patients.
Delaware, Illinois, Maryland, Ohio and Washington DC have reported record numbers of hospitalised COVID patients in recent days.
The US Centers for Disease Control and Prevention on Tuesday recommended shortening the interval between Pfizer-BioNTech's second COVID-19 vaccine dose and the booster shot to five months from six, a day after the Food and Drug Administration made a similar move.
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