The trade ministry said in a statement it would sell 37.8 million shares, which correspond to around 9.88 percent of the airline's capital, to "institutional investors".
"The Norwegian state is not a long-term owner of SAS," it added.
The sale will earn the Norwegian state around 652 million Swedish kronor (around 450 million Danish kroner), Ritzau reports.
Both Norway and Sweden have previously stated their intentions to sell off their shares in the airline, but Tuesday's shares sales mark the end of a decades-long collaboration between the Norwegian, Swedish and Danish governments over the majority ownership of the airline.
SAS noted in a press statement Tuesday that Norway had signalled its intention to leave the company some time ago, but declined to comment further on the sale, Ritzau writes.
Sweden has previously said it also planned to sell its remaining 14.8 percent stake in the company.
Denmark currently owns 14.2 percent of the shares in SAS.
“The government has made it clear that the state did not want to continue part-ownership of SAS in the long term,” Norwegian minister for trade and industry Torbjørn Røe Isaksen told NTB.
“Parliament has given the government dispensation to sell the shares on a number of occasions. We now want to make use of that,” Isaksen added.
Danish finance minister Kristian Jensen said that Copenhagen had no intention of selling its part of SAS following the Norwegian announcement.
“Norway's exit marks the beginning of a new epoch in the company's history. But that does not change the Danish state's position on ownership of SAS. There is still political support for state ownership of SAS,” Jensen told Ritzau.