Yair Netanyahu and Sandra Leikanger. Photo: Facebook
Norwegian newspaper Dagen first reported that Sandra Leikanger, from Grimstad in southern Norway, was dating Yair Netanyahu, 23, while she was studying in Israel.
"It's a big problem," Nissim Zeev, a member of the ultra-Orthodox Shas party, told the Jerusalem Post "I bet it pains him."
He called on Netanyahu to "display national responsibility" as prime minister.
Dagen reported that Netanyahu had told his Norwegian counterpart Erna Solberg that the couple had recently holidayed in Norway, when the two met at a meeting in Davos, Switzerland.
Moshe Feiglin, a hardline MP for Netanyahu's ruling Likud party, told the Jerusalem Post that 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.