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.
Danish police arrested Chung on Sunday night for overstaying her visa, Korean prosecutors said, adding they were in talks with Danish authorities to have her deported to Seoul.
Chung was arrested in the northern town of Aalborg after a tip-off from a Korean journalist, Danish police said in a statement on Monday.
At a court hearing at 1pm on Monday, police would ask that Chung be detained "until the issue of extradition is decided upon".
Danish police said Chung was aware that South Korean authorities wanted to talk to her. She was in the country "in connection with equestrian sports".
Choi, a secret confidante of Park, is accused of using her ties with the president to force top firms including Samsung to "donate" nearly $70 million to non-profit foundations Choi then used as her personal ATMs.
She is also 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 and prosecutors sought to question Chung over her admission to Ewha Women's University in 2014.
Park stands accused of colluding with Choi to extract money from the firms and also of letting her meddle in state affairs including nominations of top officials, but the president denies all charges against her.
Parliament voted on December 9th to impeach Park over the scandal and her executive powers have been handed to an acting president, Prime Minister Hwang Kyo-Ahn.
The impeachment case is being considered by the Constitutional Court -- which has up to six months to reach a ruling -- but hundreds of thousands of South Koreans have joined weekly protests calling for Park's immediate departure from office.
If the impeachment is confirmed, a presidential election will have to be held within 60 days.
Choi, daughter of a controversial religious figure who was close to Park until his death in 1994, is awaiting trial on charges including coercion and abuse of power.
Several professors at Ewha Women's University, including a former school president, have been investigated for giving Chung preferential treatment.
One professor was arrested over the weekend for allegedly giving Chung a good grade for a class she never attended and forcing his teaching assistants to forge exam records for her.
Top Samsung managers were also investigated as part of the scandal, following accusations the firm indirectly bankrolled Chung's equestrian training in Germany in a bid to curry policy favour.