The protest comes after Park Geun-hye ordered 10 of her senior advisers to quit after admitting she had allowed an old friend to edit political speeches.
Choi Soon-sil, who holds no government job, is also suspected of meddling in policy-making and exploiting her links with the president for financial gain.
Park Geun-hye’s televised apology over the scandal last week sparked widespread accusations of mismanagement.
Police said about 8,000 protesters took to the streets of Seoul on October 29. Organizers said some 20,000 people turned out.
Many held posters reading “Step down, Park Geun-hye”.
“Park has lost her authority as president and showed she doesn’t have the basic qualities to govern a country,” opposition politician Jae-myung Lee was quoted as saying by the Associated Press.
Park Geun-hye’s TV apology failed to defuse the situation.
The scandal has badly eroded the president’s popularity before next year’s elections, with some opposition parties calling on her to resign.
However, the row has not prevented Park Geun-hye from proposing that presidents be allowed to stand for a second consecutive term.
Park Geun-hye, 64, became the first woman to lead South Korea after winning presidential elections in 2012.
Choi Soon-sil is the daughter of shadowy religious cult leader Choi Tae-min, who was Park Geun-hye’s mentor until his death in 1994.
She left the country last month and is currently in Germany. She has denied in an interview with South Korean media benefiting financially from her government links.
Choi Soon-sil’s lawyer said she was well aware of the “gravity” of the situation and was willing to return to South Korea if summoned by prosecutors.
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