Yoon, who is facing a criminal trial on insurrection charges over the martial law declaration in December, was arrested in January after resisting authorities trying to take him into custody, but was released after 52 days on technical grounds.
"Detention request is related to allegations of abuse of power and obstruction of justice," the special prosecutors investigating the 2024 declaration said in a statement on Sunday.
The spokesperson for the special prosecutors declined to elaborate when asked why the detention request was submitted, saying they would explain it in court proceedings to determine whether it should be granted.
Yoon's lawyers said in a statement the special prosecutors had not provided credible evidence for the charges they were seeking, and his legal team would "explain in court that the request for an arrest warrant is unreasonable".
Yoon has been accused of mobilising presidential guards to stop authorities from arresting him in January, but the court has previously dismissed the request for an arrest warrant after Yoon initially refused to appear for questioning.
Yoon was ousted in April by the Constitutional Court, which upheld his impeachment by parliament for a martial law bid that shocked a country that had prided itself on becoming a thriving democracy after overcoming military dictatorship in the 1980s.
The December 3 decree had been lifted after about six hours when lawmakers, who had been forced to scale the walls of the assembly building to make it through a ring of security forces, voted it down.
The former president is fighting the charges against him that include masterminding an insurrection, which is punishable by death or life in prison.
He rejects the allegations.
The special prosecutor - appointed just days after liberal President Lee Jae-myung took office on June 4 following his victory in a snap election called after Yoon's ouster - leads a team of more than 200 lawyers and investigators.
Yoon attended hours of questioning by prosecutors on Saturday.
