"We're following the necessary procedures for relieving her from the post as it's not suitable for her to carry out her duties because of the scandal," a Foreign Ministry official told AFP.
Kelley, a 37-year-old Tampa woman who organised events for US military officers, was appointed as an honorary consul in August following a recommendation from the South Korean embassy in the United States.
Kelley's complaint that she had received threatening emails triggered the FBI inquiry which uncovered Petraeus' affair with his biographer, 40-year-old military reservist Paula Broadwell.
Investigators traced the mails to an anonymous account run by Broadwell, and found sexually-explicit messages from the married Petraeus.
Kelley's title carried no official responsibilities, but she was not shy about putting her influence in the spotlight. Vanity license plates on her Mercedes read "honorary consul".
In a call to Florida police after the scandal broke, she complained that reporters were trespassing on her property and infringing her diplomatic "inviolability".
Honorary diplomats have no diplomatic immunity or special protection.
During a visit to Washington on Monday, South Korean Deputy Foreign Minister Kim Kyou-Hyun suggested Kelley had abused the trust placed in her.
"It's not suitable to the status of honorary consul that (she) sought to be involved in commercial projects and peddle influence," Kim was quoted by Yonhap news agency as saying.
South Korea has 15 honorary consuls in the United States.
Their mission is to help promote South Korea-US relations and protect the rights of Korean-Americans. An honorary consul reportedly gets paid about $2,500 a year.