The plane was seen resting on grass on Monday morning next to the runway with its evacuation slides still deployed and the Thai Airways name and logo hastily covered up.
"Sparks were noticed from the vicinity of the right landing gear near the engine; the matter is under investigation," the airline said in a statement.
"The captain took control of the aircraft until it came to a complete stop and passengers were evacuated from the aircraft emergency exits. The operation was conducted by the captain and cabin crew strictly according to emergency procedures."
About 14 people were slightly injured when they escaped down the emergency slides, Thai Airways president Sorajak Kasemsuvan told local television.
"They were sent to hospital but most of them received treatment and were discharged," he added.
The carrier said it would take about 24 hours to remove the aircraft, which could cause flight delays.
The incident comes just over a week after dozens of passengers and crew were injured when a Thai Airways A380 superjumbo hit severe turbulence during a flight from Bangkok to Hong Kong.