Detention warrants are issued when the court believes there is a risk of flight or evidence tampering by suspects while investigations are ongoing.
A probe by the Transport Ministry concluded that Cho abused flight attendants in the Dec. 5 incident at John F. Kennedy airport in New York, and airlines officials may have tried to cover up the incident.
Public outrage grew when Korean Air initially issued what many in the country took to be a half-hearted apology that instead appeared to rationalize Cho's conduct in the face of what it said was inadequate performance by the cabin crew.
Cho resigned from all her posts at the airline and subsidiaries and apologized after she came under intense public outrage and ridicule. The airline's chairman Cho Yang-ho subsequently apologized and said her daughter's conduct was "foolish".
The plane pushed away from the airport departure gate as the incident was taking place on board. The pilot then brought the plane back to the gate to expel the cabin crew chief, after Cho complained about being served macadamia nuts by a flight attendant in a bag and not on a dish.
The crew chief said in a local television interview that Cho swore at him and jabbed his hand with a document folder, pointing her finger at him while he kneeled to apologize to her.
The prosecutors are also investigating whether Cho physically assaulted any of the crew members.