A house caretaker found Jett, 16, unconscious in a bathroom late Friday morning. He was taken by ambulance to a Freeport hospital, where he was pronounced dead, Police Superintendent Basil Rahming said in a statement.
The teenager had last been seen entering the bathroom on Thursday and had a history of seizures, according to the statement. An autopsy is planned.
Jett apparently hit his head on the bathtub, said a police officer who declined to be named because she was not authorized to speak on the matter.
Family attorney Michael Ossi said in a statement that Jett died suddenly on Friday. Publicists Samantha Mast and Paul Bloch released the statement but could not be reached for additional comment.
Jett was the oldest child of Travolta, 54, and his wife, actress Kelly Preston, 46, who also have an 8-year-old daughter, Ella Bleu.
Preston and Travolta have said that Jett became very sick when he was 2 years old and was diagnosed with Kawasaki disease, an illness that leads to inflammation of the blood vessels in young children. She blamed household cleaners and fertilizers, and said that a detoxification program based on teachings from the Church of Scientology helped improve his health, according to People magazine. Both Travolta and Preston are practicing Scientologists.
"I was obsessive about his space being cleaned. We constantly had the carpets cleaned," Travolta said in a 2001 interview with CNN's Larry King, a portion of which was rebroadcast on the "Larry King Live" show Friday night. During that interview, when Jett was 9, Travolta spoke of how his son nearly died when he was 2.
It is unclear whether Jett was taking any medications for his seizures.
The Scientology Celebrity Center in Los Angeles declined to comment.
A spokeswoman for Rand Memorial Hospital in Freeport said she could not release any information because of privacy concerns.
The family had arrived in the Bahamas on a private plane Tuesday and was vacationing at their home in the Old Bahama Bay resort community.
"The Travolta family has become like family to us at Old Bahama Bay and we extend our deepest sympathies to them," said Robert Gidel, president of Ginn Resorts, the property's owner.
Travolta's corporate and commercial attorney, Michael McDermott, said the actor had a very strong relationship with his son.
"There was unspoken communication between the two. ... It's just so hard," he said in a telephone interview with The Associated Press. "Kelly is very quiet and both are grieving."
McDermott said his family and other friends are with the couple in the Bahamas. The group came for a two-day New Year's celebration and had planned to return to Florida on Sunday.
"We're are all here and trying to help in any way we can," McDermott said. "Their pain is so evident."
Obie Wilchcombe, a parliament member and former tourism minister in the Bahamas, said Travolta "spent a tremendous amount of time with Jett."
"He always brought him along. There was a close affectionate relationship and lots of love," Wilchcombe told "Larry King Live" in a live telephone interview. "People in the old Bahama community today are in shock."
Wilchcombe said that an autopsy is planned for Monday, and "we expect a quick resolution."
"John spoke with the minister of health and the doctors and police are at the hospital. They're very, very quick to resolve things," he said.
Travolta, who gained fame as Vinnie Barbarino on the 1970s television show "Welcome Back, Kotter" and the 1977 film "Saturday Night Fever," went on to become one of Hollywood's biggest names. He married Preston in 1991.
A television actress, Preston appeared with Travolta in the 2000 film "Battlefield Earth," based on a novel by Scientology founder L. Ron Hubbard.
Wilchcombe said the Travoltas had invited 60 friends for the New Year's holiday weekend.
"They're needed today more than ever before," he said.
Associated Press Writers Josh Dickey in Los Angeles, Lisa Orkin Emmanuel in Miami and Kathy Corcoran in Mexico City contributed to this report.