Police Col Sompong Thip-apakul said the accident occurred on the Ao Nang Princess 5 ferry traveling from Krabi to Phuket, two of Thailand's most popular beach resort areas.
He said a 12-year-old Western child was missing but was thought to have been rescued by another boat that was going to Phuket.
Most of the rescued passengers and crew were taken to Krabi, several miles (kilometers) from where the fire occurred.
Thailand's tourism industry has suffered recently from domestic political violence and several high-profile killings and unexplained deaths of Westerners, but serious marine accidents are uncommon.