The Norwegian royal will spend a few days in a hospital in the capital for the operation on her herniated disc.
The 40-year-old will then undergo a rehabilitation programme. She has had to cancel a visit to Atlanta in the US as a result.
The Palace announced that she would be taking time off a few weeks ago. She won't return to her official duties until after Christmas.
The mum-of-three had to cancel a trip to Finland in October where she was due to meet the country's president Sauli Niinistö. Prince Haakon, travelled alone instead.
"This is a continuing challenge for the Crown Princess, and it cannot be excluded that the period will be extended," her press officer Marianne Hagen said of her sick leave. "The Crown Princess will still attempt to attend some events during the period."
Mette-Marit has suffered from neck and back problems since she had a fall in the Ukraine in 2008.
She tripped up and knocked her head on a cobbled street and was left with severe concussion. Most of the trip had to be cancelled as a result.
In 2010 the blonde royal missed the Olympics in Vancouver when her neck problem recurred.