A SAS spokeswoman told Danish news agency Ritzau that Trump's hotly-debated ban “has meant changes for our personnel”.
“We are moving personnel with dual citizenship who can have problems entering the US over to other routes,” Mariam Skovfoged said.
“It is comprehensive work, but we are of course doing it because we follow the laws and rules that are in place,” she added.
Trump on Friday signed an executive order banning citizens from the Muslim-majority countries Iran, Iraq, Libya, Somalia, Syria, Sudan and Yemen from entering the United States for 90 days.
Additionally, Trump suspended the US refugee resettlement programme for 120 days and put an indefinite stop to the acceptance of Syrian refugees.
The Danish Foreign Ministry has confirmed that Danes who also have citizenship from the seven blacklisted countries are also affected by the entry ban.
SAS's Swedish spokesman, Ferdrik Henriksson, said that there have been two cases thus far when a Sweden-based flight was forced to change personnel to comply with the new rules.
Norway-based flight personnel are likely to be less affected by the rules as Norwegian immigration law only allows for dual citizenship in certain limited circumstances.
However, a Danish spokesman for budget carrier Norwegian said that the airline is also acutely aware that the new US regulations apply to flight crew as well.
“We are closely following the situation and responding to the information that is coming from the American authorities,” Daniel Kirchhoff told Ritzau.
SAS has announced that it will refund tickets purchased before January 28th by any dual citizens who are affected by Trump's executive order.
SAS is partially owned by the Danish, Norwegian and Swedish states. Sweden owns 17 percent of the airline, while Denmark owns 14 percent and Norway 11 percent.