The anti-immigration Progress Party is objecting to Hassan Ali Khaire holding dual nationality, The Local reported.
Whereas the overwhelming majority of countries in Europe allow dual nationality, including the rest of Scandinavia, it is outlawed in Norway.
Mr Khaire, 46, arrived in Norway in the late 1980s and was able to become a dual national because Somalis are exempt from the ban.
Mazyar Keshvari, the Progress Party’s immigration spokesman, said Mr Khaire’s appointment as prime minister meant he should surrender his passport.
“He should be deprived of his Norwegian passport,” Mr Keshvari told Norwegian broadcaster NRK.
“A country’s prime minister cannot have multiple nationalities. If conflicts occur, where they will their loyalties lie?
“When someone has been appointed a Member of Parliament and even the Prime Minister of Somalia, we have to assume that they are Somali nationals,” he said.
“The fact that he has now become Prime Minister clearly shows that his need for protection should be seen as temporary and not permanent in nature.”