“More cases are expected,” the Oslo Municipality said in a statement.
“Effective tracing is being done to limit transmission routes and prevent major outbreaks.”
The Norwegian Institute of Public Health said that those affected live in Oslo and surrounding municipalities, and “the infection detection team in Oslo has contacted the municipalities concerned to start infection detection”.
The government agency said that there was “a high vaccination coverage” in the group, adding that overall “more than 50 cases” have been recorded in Norway.
The country’s first two cases were announced Monday.
On Wednesday the city of Oslo urged people who visited two restaurants in the capital to be tested.
One reportedly was where the Christmas party was held.
Much remains unknown about the new variant, including whether it is more contagious, as some health authorities suspect, whether it makes people more seriously ill, and whether it can thwart vaccines.
It is customary in Scandinavia for companies, associations and individuals to hold Christmas parties in the weeks leading up to Christmas eve.