Heather Cho, whose Korean name is Cho Hyun-ah, resigned Tuesday from the airline's catering and in-flight sales business, and its cabin service and hotel business divisions, an airline spokesman said.
But she is keeping her title as a vice president of the national carrier, he said.
As for the next steps, the spokesman told CNN there is an investigation going on, so "we will have to see."
The incident occurred Friday at New York's JFK airport on a flight due to take off for the South Korean city of Incheon.
Cho reportedly demanded that the plane go back to the gate so the crew member who served her macadamia nuts out of a bag rather than on a plate in First Class could be kicked off the flight.
Although her role put her in charge of in-flight service, she was only a passenger on this flight and was not flying in an official capacity.
According to South Korean news agency Yonhap, Cho is the eldest daughter of Korean Air's chairman, Cho Yang-ho.
He apologized Tuesday for any inconvenience caused to passengers and said the incident would be investigated, the news agency reported.
Korean Air also issued an apology on Heather Cho's behalf, Yonhap reported, in which she asked for forgiveness. "I will take full responsibility for the incident and step down from my post," she is quoted as saying.
Korean Air apologized for any discomfort to those on the flight and said there had been no safety issues involved. The plane arrived at its destination only 11 minutes behind schedule, according to Yonhap.
"Even though it was not an emergency situation, backing up the plane to order an employee to deplane was an excessive act," the airline said in a statement.
"We will re-educate all our employees to make sure service within the plane meets high standards."
According to her biography on the website of Nanyang Technological University
, Heather Cho joined the airline in 1999 and has since been "actively involved in establishing a new corporate identity for Korean Air."
She studied at Cornell University and the University of Southern California.