Yoon on Wednesday became the first sitting South Korean president to be arrested and was taken to the Seoul Detention Centre, after refusing to co-operate.
He remained in the centre on Thursday, with his lawyer citing his health as a factor.
Authorities have 48 hours to question the suspended president, after which they must release him or seek a warrant to detain him for up to 20 days.
Yoon's refusal to co-operate with investigators comes as the Constitutional Court held a second hearing in his impeachment trial to determine whether to remove him permanently or reinstate his presidential powers.
Yoon Suk-yeol said he turned himself in to prevent the risk of "unsavoury bloodshed". (AP PHOTO)
South Korea is grappling with its worst political crisis in decades, sparked by Yoon's brief attempt to impose martial law on December 3 that was voted down by parliament.
In opening arguments at the Constitutional Court, an opposition Democratic Party MP condemned Yoon for "the December 3 insurrection", and said Yoon and a small number of supporters had sought to stoke chaos by refusing to accept his arrest warrant.
"This impeachment trial decides whether or not to bring someone like this back to the position of commander-in-chief in control of the military," said Jung Chung-rae, who heads parliament's legislation and judiciary committee.
In response, one of Yoon's defence team said his impeachment was not intended to defend the constitution but for the opposition "to use the majority power of parliament to usurp the position of the president".
The main opposition Democratic Party used its majority in parliament to bring on Yoon's impeachment vote, although 12 MPs from Yoon's own party also voted to impeach.
Yoon's lawyer Cho Dae-hyen said the suspended president's decision to declare martial law had been made in good faith based on his view that the country was in a state of emergency.
Yoon's arrest on Wednesday ended a weeks-long stand-off with authorities after hundreds of police swooped before dawn on his fortified villa in Seoul.
Hundreds of police swooped before dawn on Yon Suk-yeol's Seoul villa to detain him for questioning. (AP PHOTO)
Yoon said he turned himself in for questioning to prevent what he called the risk of "unsavoury bloodshed", though he continued to protest that it was an illegal investigation and invalid arrest warrant.
The embattled leader has up to now refused to talk with investigators who had prepared a questionnaire of more than 200 pages, an official from the Corruption Investigation Office for High-ranking Officials (CIO) that is heading the criminal inquiry said.
His questioning had been due to resume on Thursday afternoon, but the CIO said Yoon's side had told the agency he would not attend.
Yonhap cited Yoon Kab-keun, one of Yoon's lawyers, as saying the suspended president's health was a factor and saying further questioning was pointless.
A small crowd of protesters supporting Yoon gathered outside the CIO office, calling the president's arrest illegitimate.
His lawyers have said the arrest warrant is illegal because it was issued in the wrong jurisdiction and the investigators had no legal mandate.
His legal team has denied allegations against Yoon of masterminding insurrection, a crime in South Korea punishable by life imprisonment or even the death penalty.
