The deputy governor of Phuket island said he feared at least 100 passengers could have been killed.
The MD-82 aircraft, operated by budget carrier One-Two-Go, was flying to Phuket from the capital, Bangkok.
Thai television broadcast images showing the crumpled fuselage of the plane.
Foreign casualties
The MD-82 aircraft was flying to
Phuket from the capital, Bangkok
Foreign tourists were among those believed to have lost their lives.
Hospital officials said that British, Australian, Thai, Irish and Iranian citizens were among those who survived the crash.
Chiasak Angkauwan, a civil aviation official, told Thai television: "The first part of the plane is dug into the ground. The tail section is stuck on the runway.
"The airplane asked to land, but due to the weather in Phuket - strong wind and heavy rain - maybe the pilot did not see the runway clearly."
Lieutenant-Major Sokchai Limcharoen, a police chief in the Phuket area, said the aircraft crashed at 3:35pm (0835 GMT).
"The plane was landing and slid off the runway. We are rescuing people and carrying injured people to hospitals," he said.