Isaksen's ministry announced on Tuesday that it would sell 37.8 million shares, which correspond to around 9.88 percent of the airline's capital, to "institutional investors".
The sale will earn the Norwegian state around 652 million Swedish kronor (around 597 million Norwegian kroner), Ritzau reports.
No information has yet been released as to the identity of the buyer or buyers.
“We have owned 9.88 percent of SAS and have made it known for some time that we did not see ourselves as long-term owners,” Isaksen told Norwegian broadcaster NRK.
Speaking on NRK's Nyhetsmorgen programme, the minister said that justification for Norwegian state ownership of SAS had changed.
“We ensure that there are flights to where people live in a completely different way today. The other reason is that the government's position is that ownership in the private sector is important but there must be a special reason for it,” he said.
“When there is no longer any reason for us to own, we sell our share,” he continued.
SAS was founded in 1946 as a joint Scandinavian effort to increase air traffic between the Nordic region and North and South America.
The minister went on to say that he did not believe the sale would affect Norwegian jobs.
“We owe shares for various reasons. We own a lot of Equinor [petrol and energy company, formerly Statoil, ed.] because we want the base of the company to be in our country, but the ownership of SAS has been about getting as much as possible for our investment,” he said.
After a number of difficult years for SAS, the airline has seen a recent upturn in fortunes with profits of 1.4 billion Swedish kronor announced last year.
With the government's main objective ensuring a return for its share, it was expected that a sale would come soon, Prime Minister Erna Solberg said to NRK on Tuesday.
“Our assessment is that this is a very reasonable price compared to the value of other airlines. It was a good and correct time to sell,” Isaksen said to the broadcaster.
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