A Seoul court approved the request for an arrest warrant, saying it was "concerned" that Yoon might "destroy evidence."
A South Korean court extended President Yoon Seok-yeol's detention to up to 20 days, prompting violent protests by hundreds of angry supporters who stormed the court building, smashing windows and breaking in.
Shortly after the verdict was announced in court at around 3am on Sunday (18:00 GMT on Saturday), his supporters swarmed the building, overwhelming riot police who tried to stop them.
Yoon last week became the first sitting South Korean president to be arrested as he faces rebellion charges related to the short-lived and shocking martial law order on December 3 that plunged the country into political turmoil.
Video showed protesters firing fire extinguishers at a line of police officers guarding the front door before swarming inside, destroying office equipment and furniture.
Yin and his lawyers appeared before a court judge at a hearing on Saturday and argued for his release. His arrest could signal a lengthy stay in custody, lasting several months or more.
He faces potential rebellion charges for declaring martial law on December 3, triggering the country's worst political crisis since democratization in the late 1980s.
The Office for the Investigation of Senior Officials' Corruption, which is investigating jointly with police and the military, can now extend his detention to 20 days, during which time they will hand the case over to prosecutors for prosecution.
Yin's lawyers can also file a petition challenging the court's arrest warrant.
The leader is expected to remain in a separate cell at a detention center in Seoul.
"President Yoon and our legal team will never give up," a lawyer representing Yoon, who said the criminal investigation was ineffective, said in a statement.
"We will do our best to right the wrong in all future judicial proceedings," the lawyers said, adding that the violence in the courtroom was an "unfortunate" incident.
Yoon's conservative People's Power Party (PPP) called the court's decision "very regrettable."
"There is a question as to whether the consequences of detaining a sitting president have been adequately considered," the party said in a statement.
But the main opposition Democratic Party called the court's approval of the arrest warrant a "cornerstone" for re-establishing order and said "riots" by "far-right" groups would only deepen the national crisis.
The Popular Party's support collapsed after he declared martial law, then revoked it hours later as parliament voted unanimously to reject it. On December 14, members of Congress impeached Yoon, suspending his presidential powers.