Chung Yoo-Ra, the 20-year-old daughter of the woman dubbed South Korea's "Rasputin", is one of the figures in the influence-peddling scandal that led to huge street protests demanding the removal of President Park Geun-Hye.
Chung was detained in Denmark on January 1 for overstaying her visa, after South Korean authorities issued a warrant for her arrest.
Seoul then sought her extradition, which the Danish public prosecution authority approved on March 17. Chung then took her case against extradition to the Aalborg district court.
"The district court confirms decision from the Director of Public Prosecutions. Ms Chung is to be extradited," the prosecution authority wrote on Twitter.
The District Court confirms decision from the Director of Public Prosecutions. Ms. Chung is to be extradited. Appeal is filed #anklager— Rigsadvokaten (@Rigsadvokaten) April 19, 2017
Prosecution spokesman Simon Gosvig told AFP that Chung, who has denied any wrongdoing, had immediately filed an appeal with the court in Aalborg.
"We would like another result saying she's not to be sent to South Korea, so we made an appeal right away to the High court," Chung's lawyer Michael Juul Eriksen told AFP outside the Aalborg district court.
Eriksen said Chung's main fear was losing contact with her infant son because she had been "pressured" and "threatened" by the Korean authorities to collaborate in the case.
"If we could get some guarantee that she would not lose contact with her son... that could also solve the problem because then she would be willing to go back freely," Eriksen said.
An equestrian who has reportedly bought horses and trained in Denmark in the past, she has told police she was in Denmark because of her involvement in the sport.
Chung's mother, a confidante of Park's, is accused of using her influence to secure her daughter's admission to an elite Seoul university, with a state probe revealing that the school had admitted her at the expense of better-qualified candidates.
The revelation touched a raw nerve in education-obsessed South Korea. Several professors at Ewha Womans University, including a former school president, have been investigated for allegedly giving Chung preferential treatment.
A South Korean special prosecutor is also probing allegations that Chung's mother used millions of dollars of bribes from Samsung, South Korea's largest conglomerate, to finance her daughter's equestrian career and luxurious lifestyle in Europe.
Prior to Wednesday's hearing, Eriksen told Danish news agency Ritzau he would argue that his client had not committed any crime and that the extradition was politically motivated.
"We think this is a political case, and therefore there can be no extradition," he said.
Ousted South Korean President Park Geun-Hye was on Monday charged with bribery involving millions of dollars over the massive corruption and influence-peddling scandal that brought her down and which has also implicated top businessmen.
The former leader, already detained at a centre near Seoul, also faces charges of abusing her powers and leaking state secrets.
Park is accused of colluding with her confidante, Chung's mother Choi Soon-sil, who is already on trial for coercing local conglomerates into donating a total of 77.4 billion won ($68 million) to two non-profit foundations.
Choi allegedly used some of the donations for personal gain.