A Spanish woman, Pilar Abel, says the painter is her father. She says he had an affair with a maid in 1955.
In ordering the exhumation, the judge said there were no biological remains or personal objects of the artist to be used in the paternity test.
The surrealist painter died in Spain in 1989, aged 85.
He was buried in his home town of Figueres in north-eastern Catalonia region of Spain.
Maria Pilar Abel Martínez, a tarot card reader who was born in Girona made the claim for the first time in 2015.
She said her mother had worked for a family that spent time in Cadaqués, next to where the painter had a home, Spanish newspaper El País reports (in Spanish).
At that time, Dalí was married to Gala. The couple had no children.
The Gala Dalí Foundation has not commented.