SEOUL, South Korea — The woman at the center of President Park Geun-hye’s worst leadership crisis was jailed on Tuesday, as prosecutors grilled her overnight over allegations that she had manipulated important government affairs from the shadows.

Choi Soon-sil, 60, a friend of Ms. Park’s for 40 years and widely seen here as the president’s secret adviser, though she had no official government title, was also accused of using her influence to extort $69 million from big businesses in the form of donations to two foundations she controlled.

On Sunday, Ms. Park fired eight aides, including her chief of staff, in an effort to regain public trust. That was a day after thousands of South Koreans took to the streets to call for her removal from office.

And on Monday, after weeks of evading the news media and public scrutiny, Ms. Choi presented herself to prosecutors. She tearfully apologized before a phalanx of television cameras, while angry citizens demanded her arrest. One person was detained while attempting to hurl a tub of excrement at her and the prosecutors’ office, claiming that the investigation was rigged to protect Ms. Park.