Yoon briefly suspended civilian rule this month, plunging South Korea into its worst political crisis in decades.
He was stripped of his presidential duties by parliament over the action, but a constitutional court ruling is pending on whether to confirm the impeachment.
The conservative leader also faces criminal charges of insurrection, which could result in life imprisonment or even the death penalty.
A former prosecutor himself, Yoon had been summoned three times by investigators for questioning, but refused to present himself each time -- including by yesterday's deadline.
"The Joint Investigation Headquarters filed an arrest warrant for President Yoon Suk Yeol with the Seoul Western District Court", said the probe team in a statement.
The application by investigators marks the first attempt in the country's history to forcibly detain a president before the impeachment procedure is complete.
Yoon is being investigated by prosecutors as well as a joint team comprising police, defence ministry, and anti-corruption officials.
A 10-page prosecutors' report seen by AFP stated that Yoon authorised the military to fire weapons if needed to enter parliament during his failed martial law bid.
Yoon's lawyer Yoon Kab-keun had dismissed the prosecutors' report, telling AFP it was "a one-sided account that neither corresponds to objective circumstances nor common sense".
'Drag them out'
Yoon declared martial law in an unannounced televised address on December 3, saying it was aimed at eliminating "anti-state elements".
Lawmakers rushed to parliament within minutes of the declaration to vote it down.
At the same time, heavily armed troops stormed the building, scaling fences, smashing windows and landing by helicopter.
According to the prosecution indictment report, Yoon told the chief of the capital defence command, Lee Jin-woo, that military forces could shoot if necessary to enter the National Assembly.
"Have you still not got in? What are you doing? Break down the door and drag them out, even if it means shooting," Yoon told Lee, according to the report.
Yoon also allegedly told the head of the Defense Counterintelligence Command, General Kwak Jong-keun, to "quickly get inside" the National Assembly since the quorum for lifting the martial law declaration had not been met.
"So quickly get inside the National Assembly and bring out the people inside the chamber, and break down the doors with an axe if necessary and drag everyone out," the report quotes Yoon as saying at the time.
The report also said there was evidence that Yoon had been discussing declaring martial law with senior military officials as early as March.
As investigations began against Yoon, attempts by prosecutors to search his offices were blocked by the presidential security team.
South Korea's political turmoil deepened late last week when Yoon's replacement, Han Duck-soo, was also impeached by parliament for failing to sign through bills for investigations into Yoon.
Finance Minister Choi Sang-mok has taken over as the new acting president, and found himself thrust immediately into a disaster with the Jeju Air plane crash that claimed 179 lives.
