The 20-year-old Chung Yoo-ra is the daughter of Choi Soon-sil, who is jailed in South Korea on suspicion of bribery and receiving favors from companies in return for manipulating government affairs.
Chung Soo-ra, who is wanted as part of the corruption investigation, was arrested in Aalborg, northern Denmark, on January 1 on an international warrant.
A lower court last month determined that all conditions for her extradition request had been met. Wednesday's appeal hearing was scheduled to last one day.