Pilar Abel, 61, also from Figueres, has for more than a decade been fighting to prove she is Dalí's daughter, claiming to have learned from her mother and grandmother at the age of eight that she was the product of an affair with the married artist.
Despite being dismissed by many as a fraud, Ms Abel in June won a court order to exhume Dalí's body, a Madrid judge ruling there was no other way to settle the claim.
The artist's two tibias have been extracted as well as nails and teeth, and will now be taken to Madrid for testing before being replaced to preserve the integrity of the body, Lluís Peñuelas, secretary of the Gala-Salvador Dalí Foundation, said.
He stressed that the Foundation, which administers Dalí's estate, regards the exhumation as "completely inappropriate" and Ms Abel's claim as "baseless".
The exhumation was far from simple. Cranes were installed to lift the one and a half ton tombstone from Dalí's crypt, which lies beneath the stage in the artist's self-designed Theatre-Museum.
The operation took place under the cover of night, with media banned and tarpaulins placed over the top of the building to prevent drones spying from overhead.
Just 15 people were present and all phones and cameras were prohibited to prevent images leaking out.
Marta Felip, the mayor of Figueres, said it was "grotesque" that the fortune teller's claim had been taken so far.
She said the results would be known in the first week of September, and said that if Ms Abel was found not to be the artist's daughter, the Foundation and the local government would be seeking to recover their considerable costs.
But if Ms Abel is proved right, she could be entitled to a 25 percent share of Dalí's considerable estate. That will open up another legal battle with the Foundation and the Spanish state, to which he left his works.
"The question of tracing any inheritance will be a difficult one," Michael Mylonas QC of London barristers' chambers Serjeants' Inn told The Telegraph, suggesting that the Foundation "must be feeling some heat".
Ms Abel told the Telegraph that she was unconcerned by the criticisms, and dismissed the Dalí Foundation's questioning of the court order as "pathetic".
"I am very happy because at last it's going to come to light, and this means a lot, it doesn't matter to me what the Foundation says," she said.
She insisted that she was not motivated by any potential inheritance but by a desire to know who she was. "It's about my identity, and nothing else," said Ms Abel, adding that the first thing she would do if the test came out positive was change her name. But then, she acknowledged, "probably I am going to ask for what is mine".
The fortune teller, who for eight years hosted a tarot card reading show on local television, claimed that the visionary Dalí was the source of her powers. "I have had this gift since I was little, and where else can it come from? It can't be from anyone else but him."
Ms Abel said she believed the artist knew she was his child, relating an encounter told to her by her mother Antonia, who has given her blessing to the paternity suit. Her mother was pushing her in a pram when the pair ran into Dalí; he allegedly patted her head and remarked "So this is my daughter Pilar, eh?". Ms Abel had crossed paths with him again as a teenager, and the pair had exchanged "looks that were more than looks", she said.
Shrugging off suggestions of an unseemly spectacle, the fortune teller said she was happy to have put Dalí back in the news. "It is what I wanted, to lift him up again. He deserves it. A great genius, a great person, and a great painter."
