Airport officials were notified at 7:15 p.m. Tuesday of the alleged threat to Los Angeles-bound Flight 794, FBI spokeswoman Laura Eimiller said.
The plane landed safely after 8 p.m. and was taken to a remote area of the airport, where passengers exited the plane.
Thai Airways president Piyasvasti Amranand told The Associated Press that the message -- written in English with bad grammar -- warned that a bomb was on the plane.
"This must have caused some nuisance to the passengers," he said by phone from Singapore. "It sounds like it was done by a crazy person."
Eimiller said there were about 200 passengers and crew on board.
Luggage on the plane was to be screened and the passengers and crew were being interviewed by law enforcement officers, she said.
The Los Angeles Fire Department said there were 18 fire trucks and fire engines on standby when the plane landed.
The Associated Press contributed to this report.