Norwegian newspaper Dagen reported that Yair Netanyahu, 23, was dating 25-year-old Norwegian Sandra Leikanger, currently studying in Israel.
Dagen said that at a meeting in Davos, Netanyahu had told his Norwegian counterpart Erna Solberg the two had recently holidayed in Norway.
Nissim Zeev, a member of the ultra-Orthodox Shas party, told the Jerusalem Post on Sunday Netanyahu must "display national responsibility” as prime minister.
"It's a big problem,” he said. "I bet it pains him.”
MP Moshe Feiglin, a hardline member of Netanyahu's ruling Likud party, told the Jerusalem Post the relationship "is very unfortunate”.
The paper cited a source close to Netanyahu's son as confirming that Leikanger is not Jewish.
The extremist Israeli organisation Lehava, which says it aims "to prevent assimilation in the Holy Land”, called on Netanyahu "to prevent this relationship”.
"Your grandchildren, as you know, will not be Jewish,” Lehava director Bentzi Gopshtain warned the Israeli premier in a Facebook post.
Judaism is traditionally matrilineal, in which a child's religion is determined by that of its mother.
Yair is the son of Netanyahu's third wife, Sara. Netanyahu was himself married to a non-Jewish woman, Fleur Cates, between 1981 and 1984.
Netanyahu's office refused to comment on Yair's reported relationship.