The teen, who reportedly had a history of health problems, was vacationing with his parents when he suffered a seizure at the Old Bahama Bay Hotel on Grand Bahama Island. Attempts to revive him were unsuccessful, Travolta's attorney Michael Ossi told the entertainment news Web site.
Police told TMZ it appears Jett hit his head in a bathtub. An autopsy was being conducted to determine the exact cause of his death.
Usmagazine.com quoted John Travolta as speaking affectionately about his son during an interview with the Australian media several years ago.
"He's my first, and he's my heart. And he's a very special boy," John Travolta said. "He's Daddy's boy."
Ossi told CNN Jett's death "was completely out of the blue."
"John and Kelly are happy when their children are happy. This is the worst day of John's life," the lawyer said.
Preston's half-brother, Chris Palzis, told OK! magazine: "We're all devastated. It's definitely a bad time. That's all I have to say."
In addition to his parents, Jett Travolta is also survived by an 8-year-old sister named Ella.
John Travolta is best known for his roles in the movies "Saturday Night Fever," "Grease," "Pulp Fiction" and "Primary Colors." He recently lent his voice to the title character in the animated movie "Bolt."
Preston's film credits include "Secret Admirer," "SpaceCamp," "Jerry Maguire," "What a Girl Wants" and "The Cat in the Hat."