Kim, who offered his resignation on Wednesday, was seen as a central figure in Tuesday's brief martial law declaration.
A senior military official and filings to impeach Yoon by opposition members said Kim had made the proposal to Yoon.
The declaration of martial law plunged South Korea into its greatest political crisis in decades. (AP PHOTO)
Yoon survived an impeachment vote in parliament on Saturday, prompted by his short-lived attempt to impose martial law, but the leader of his own party said the president would eventually have to step down.
The prosecution's special investigative team has questioned Kim, who voluntarily appeared at the Seoul Central District Prosecutors' Office at around 1:30am on Sunday (3:30am AEDT), the report said.
The office was not immediately available for comments.
Three minority opposition parties filed a complaint with the prosecution against Yoon, Kim and martial law commander Park An-su, accusing them of treason.
Kim faces a travel ban as prosecutors investigate, Yonhap said.
The national police are also investigating claims of treason against Yoon and top ministers.
Yoon shocked the nation on Tuesday night when he gave the military sweeping emergency powers to root out what he called "anti-state forces" and obstructionist political opponents.
He rescinded the order six hours later, after parliament defied military and police cordons to vote unanimously against the decree.
Yoon's martial law declaration plunged South Korea, Asia's fourth-largest economy and a key US military ally, into its greatest political crisis in decades, threatening to shatter the country's reputation as a democratic success story.
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