Munch is thought to have died childless, The Local.No reported.
Janet Weber said she has come forward not because she was to claim any of the artist's fortune, but because she wants to learn more about her heritage.
"For me to know that Edvard Munch might be my grandfather is almost incomprehensible," she said.
Weber claims that Munch might have had twins with her grandmother, the violinist and model Eva Mudocci.
Mudocci gave birth to twins, Isobel and Kai, in Copenhagen in December 1908. She never revealed their father's identity to them. However, Mudocci's friend, Bella Edwards, told Weber's mother, Isobel that Munch was her father.
One of Munch's heirs, Elisabeth Munch-Ellingsen, said, "It's fun for us if it's true," that Weber is related. She volunteered to take a DNA test to confirm if it's true.