The Seoul Central District Court earlier issued a warrant to detain Ms Park while she is investigated on charges of bribery, abuse of authority, coercion and leaking government secrets.
It followed a nearly nine-hour court hearing on Thursday that Ms Park attended.
"It is justifiable and necessary to arrest [Ms Park] as key charges were justified and there is risk of evidence being destroyed," the court said in a statement.
Live television footage showed a black sedan carrying her to the detention facility from the prosecutor's office where she had been waiting.
Despite the early hour, some 50 supporters, waving national flags and demanding her release, were at the gate to greet her, the AFP news agency reports.
Ms Park can be held for up to 20 days before being formally charged.
If convicted she could face more than 10 years in prison.

Ms Park lost her presidential immunity and was dismissed from her post when the constitutional court upheld a decision by parliament in December to impeach her.
Ms Choi is accused of using her presidential connections to pressure companies to give millions of dollars in donations to non-profit foundations she controlled.
Ms Park is alleged to have been personally involved in this, and to have given Ms Choi unacceptable levels of access to official documents.
Judges had said the former president had broken the law by allowing Ms Choi to meddle in state affairs, and had breached guidelines on official secrets by leaking numerous documents.
Ms Choi and Samsung's acting head Lee Jae-yong, also involved in the scandal, are being held in the same detention centre to where Ms Park has been sent. They are also being tried separately.
Hwang Kyo-ahn, who is loyal to Ms Park, is now the acting president and an election is to be held by 9 May.