Yoon's powers will be suspended until the court rules on the case, either removing Yoon from office or restoring his powers.
The court has up to six months to decide, and if he's dismissed, a national election to choose his successor must be held within 60 days.
Parliament impeached Yoon over his short-lived attempt to impose martial law. (AP PHOTO)
Prime Minister Han Duck-soo, the country's No. 2 official, took over presidential powers late on Saturday.
Han was appointed by Yoon, whose government has struggled to pass legislation in the opposition-controlled parliament.
Lee Jae-myung, the leader of the opposition Democratic Party, told reporters on Sunday that a swift ruling is the only way to minimise national chaos.
Lee also proposed the creation of a national council where the government and the National Assembly would work together to stabilise state affairs.
He said bipartisan co-operation is essential to navigating the political paralysis that has halted high-level diplomacy and spooked financial markets since Yoon's martial law decree.
Lee also said that the Democratic Party would not seek to impeach Han, despite some calls to do so over his alleged inaction to prevent Yoon's martial law enforcement.
Lee said there was no need to introduce further political uncertainty.
"The Democratic Party will actively co-operate with all parties to stabilise state affairs and restore international trust," Lee said.
"The National Assembly and government will work together to quickly resolve the crisis that has swept across the Republic of Korea."
The declaration of martial law has caused political chaos. (AP PHOTO)
Yoon's December 3 imposition of martial law, the first of its kind in more than four decades, lasted only six hours, but has caused massive political tumult, halted diplomatic activities and rattled financial markets.
Yoon was forced to lift his decree after parliament unanimously voted to overturn it.
Yoon sent hundreds of troops and police officers to the parliament in an effort to stop the vote, but they withdrew after the parliament rejected Yoon's decree. No major violence occurred.
Opposition parties have accused Yoon of rebellion, and say that a president in South Korea is allowed to declare martial law only during wartime or similar emergencies and would have no right to suspend parliament's operations even in those cases.
The conservative Yoon rejects the charges and says he aimed to issue a warning to the Democratic Party, which he has called an "anti-state force" as it's used its control of parliament to impeach many top officials and hold up the government's budget bill for next year.
