At one point, the girl - who has not been named because she is a minor - shouts at the driver, "Hey, you! I'll speak to my mother today to make you lose your job.
"You're fired", she adds. "You're really insane. Hey, I'm speaking to you. I told you don't want to [sit down]. Why should I sit down? This is my car, not yours."
After a prolonged silence, the driver can be heard replying, "Fire me if you want".
The girl yells back, "Do you think I would be embarrassed? You're crippled. Crippled without arms, legs, face, ears or a mouth. You're insane. Your parents taught you wrong.
"I really hate you. I want you to die. That's my wish."
The driver reported the girl's comments to her parents and her mother made her apologise, before becoming hostile and demanding that he delete the recordings. Sacked the following day, he was given no reason for the decision.
Interviewed by MBC, the tearful chauffeur said, "I expected that [the mother] would console me with an apology and warm words, but that was not the case".
The incident has sparked outrage on social media, with commentators saying the heads of the nation's "chaebol" business groups and their families are "living in the Dark Ages" and that they consider anyone in the service industries to be their "personal slaves".
In December 2014, the vice-president of Korean Air and daughter of the president of the national flag carrier was roundly criticised for flying into a rage at the way an attendant served her a bag of nuts as their aircraft prepared to take off from New York's John F. Kennedy airport.
Heather Cho was accused of assaulting the flight attendant, before ordering the aircraft to return to the terminal and delaying the flight by 20 minutes.
She later resigned a number of her duties at the airline and served three months of a 12-month term for endangering aviation safety, although she has since returned to many of her posts.
Her younger sister, Emily Cho, followed in her footsteps earlier this year when she allegedly verbally abused and threw water at an employee of the airline's advertising agency during a business meeting, Yonhap reported. The Korea Times reported that she was "enraged" at the employee's work performance.
She denied throwing water but acknowledged shoving the employee, the BBC reported.