Chung Yoo-ra, 20, is accused of staying in the country illegally, they said.
Her mother Choi Soon-sil is accused of using her friendship with President Park Geun-hye for personal gain, including getting Ms Chung into a top Korean university.
After weeks of protest, parliament voted on 9 December to impeach Ms Park.
Both women have apologised while denying the accusations.
South Korean authorities had asked for Interpol's help in tracing Ms Chung after she failed to return to answer questions about her role in the scandal.
They are reportedly planning to extradite Ms Chung, a former national equestrian rider.
Her mother Ms Choi is in detention having returned from abroad to face questioning.
She has been charged with various offences, including abuse of authority, coercion, attempted coercion and attempted fraud.
South Korea's constitutional court has six months to uphold or overturn the impeachment vote against Ms Park.
Until then she remains formally president but stripped of her powers, which have been handed to the prime minister, a presidential appointee.
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