Yoon was removed by South Korea's parliament on Saturday over his short-lived attempt to suspend civilian rule, which plunged the country into its worst political turmoil in years.
The Constitutional Court has around six months to determine whether to uphold the impeachment.
Fresh elections must be held within two months if he is removed. Prime Minister Han Duck-soo is serving as interim leader in Yoon's stead.
The court formally began proceedings at 10 am (GMT 0100) on Monday, a spokesman told AFP.
A separate investigation into Yoon and his inner circle over the December 3 martial law declaration has rumbled on as the turmoil deepened.
Yoon remains under a travel ban while the probe is underway.
The prosecution said in a news release on Sunday they had summoned Yoon for questioning over the insurrection and abuse of power allegations "but he refused to comply".
They said they would issue a "second summons", with Yonhap news agency reporting that could come on Monday.
Yoon 'ringleader'
The concurrent probe by a joint police, anti-corruption office and defence ministry team is also asking Yoon appear for questioning, Yonhap said.
They reportedly accuse Yoon of being the "ringleader" of the martial law bid.
Vast protests against Yoon, with smaller rallies supporting him, have rocked the South Korean capital since his martial law decree.
Demonstrators in both camps have vowed to keep up the pressure as the Constitutional Court mulls Yoon's fate.
Police arrested both the current and former heads of the Defence Intelligence Command on Sunday in connection to the insurrection allegations, Yonhap reported.
Prosecutors said they were also seeking an arrest warrant for the head of the Army Special Warfare Command Kwak Jong-keun, according to Yonhap.
Kwak is accused of sending special forces troops to parliament during the martial law bid, sparking a dramatic confrontation between soldiers and parliamentary staff.
The head of Yoon's ruling People Power Party (PPP), who has not been linked to the martial law bid and expressed support for impeachment, resigned on Monday.
"I sincerely apologise to all the people who have suffered due to the emergency martial law incident," Han Dong-hoon told a news conference in Seoul.
In declaring martial law, Yoon vowed to "eliminate anti-state elements" and suggested the country's electoral system was vulnerable to outside interference.
Han Dong-hoon condemned on Monday "extremists such as election fraud conspiracy theorists" and warned "there will be no future for conservatism" if the party entertained those views.
"I wish for the well-being of our country," he said.
North Korea weighs in
The South Korean government has meanwhile sought to project an air of business as usual.
Acting president Han Duck-soo held a call on Sunday with US President Joe Biden, who underscored the strength of bilateral ties.
Han Duck-soo has also ordered the military to "enhance vigilance" against North Korea, with which the South technically remains at war.
North Korean state media decried Yoon as a "ringleader of rebellion" on Monday, its first reaction to his impeachment.
The state-run Korean Central News Agency (KCNA) said Yoon had attempted to shift responsibility for the "foolish emergency martial law declaration" onto opposition parties.
"The investigation into puppet Yoon Suk Yeol, the ringleader of the rebellion, and his accomplices is under way," KCNA said.
"The puppet Constitutional Court will finally decide" on whether to remove Yoon, it said.
KCNA has described the South as being "in chaos" over the martial law order.
Relations between the two Koreas have been at one of their lowest points in years, with the North launching a flurry of ballistic missiles in violation of UN sanctions.
