Chung's arrest, announced by prosecution spokesman Kang Chan-woo, came late Friday, after the Seoul District Court issued a warrant.
Prosecutors suspect the 68-year-old Chung of embezzling company funds to create a slush fund and of causing damage to the company.
Chung emerged from the Supreme Prosecutors' Office in Seoul after his arrest. He was escorted by what appeared to be two prosecution officials, and they got into a waiting car for the journey to the Seoul Detention Center, just outside the city.
He made no comment to reporters and photographers.
Seoul District Court Judge Lee Jong-seok said after deliberating all day Friday, he decided to issue the warrant because of the "heavy" nature of the allegations.
"The suspect is denying most of the charges and is feared to destroy evidence," Lee said.
Kang said prosecutors will continue to investigate Chung during his detention before issuing an indictment.
Under South Korean law, prosecutors can detain suspects after arrest for a maximum of 20 days before indictment.
"Vice Chairman and CEO Kim Dong-jin will assume full responsibility and operational control" for Hyundai Motor "a duty he shared with Chairman Chung Mong-koo," company spokesman Oles Gadacz said after the arrest warrant was issued, reading a statement.
"All local and overseas manufacturing, sales marketing and R&D operations are unaffected by today's development and will continue normal operations," Gadacz said.
Prosecutors suspect Chung of embezzling about $106 million in company money to create a slush fund, and breach of trust for allegedly incurring about $320 million in damages to the company, the prosecution said Thursday when they requested the arrest warrant.
Hyundai, which relies on exports for about 60 percent of its overall revenue, sold a record 2.53 million vehicles last year, up 11 percent from 2004. Kia sold 1.27 million vehicles, up 13.9 percent.
Prosecutors have raided Hyundai and three of its affiliates -- Kia, logistics unit Glovis Co. and auto-parts maker Hyundai Autonet -- and questioned key officials.
Prosecutors say officials embezzled money from affiliates to create the slush fund and used it, via at least two lobbyists, to seek favors from the government.
The lobbyists have been arrested on charges of receiving money from Hyundai in exchange for promises to help it win construction approvals and permits, and other business favors.
It is unclear if the lobbyists bribed government officials. It is illegal in South Korea to accept money in return for exercising influence.
Chung spent about 15 hours at the Supreme Prosecutors' Office in Seoul for questioning earlier this week. His son, Kia President Chung Eui-sun, spent about 18 hours there last week.