Department of Civil Aviation director general Voradej Harnprasert said THAI flight TG 679 Guangzhou-Bangkok left the runway while landing at about 11.30pm.
One engine of the Airbus A330-300 aircraft caught fire after landing, but airport firefighters promptly put out the blaze.
All 288 passengers and 14 crew members were safe, but 13 were reported injured in the incident and were sent to a nearby hospital.
THAI president Sorajak Kasemsuvan said the flight left Guangzhou at 9.25pm local time and arrived Suvarnabhumi airport at 11.20pm.
When the plane touched the runway, there was a glitch in the tyre system, causing the aircraft to slip off the runway, sparking the fire in the engine.
The captain successfully stopped the aircraft and passengers were evacuated safely, but with 13 of them receiving injuries.
Rawewan Netrakavesna, Suvarnabhumi Airport general manager, said the airport closed the eastern runway as the aircraft was still where it left the runway. Airports of Thailand (AoT) may consider diverting some flights to Don Mueang Airport to ease congestion.
She said an investigative team from the Civil Aviation Department has arrived the scene to probe the incident.
Ms Rawewan said the airport would evaluate the damage of the runway, but believed it could be fixed in one day.