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 sparked massive 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.
The Danish Office of the Director of Public Prosecutions has said it needs more time to complete its processing of the case, and was waiting for the South Korean authorities to answer some questions.
"The detention has been extended until March 22," a court spokeswoman told AFP. Chung has denied any wrongdoing.
The equestrian, who has reportedly bought horses and trained in Denmark in the past, has told police that she was in the country because of her involvement in the sport.
Chung's mother, a confidante of Park, is accused of using her influence to secure her daughter's admission to an elite Seoul university, with a state probe revealing the school had admitted Chung at the expense of other candidates with better qualifications.
The revelation touched a raw nerve in education-obsessed South Korea.
Several professors at Ewha Women's University, including a former school president, have been investigated for allegedly giving Chung preferential treatment.