It could not be immediately known how many people were on board the plane, which took off from New York’s Rochester city, at 08.26 a.m. (12:26 GMT). The aircraft was due to fly to Naples, Florida, before it went off course.
The plane — Socata TBM-700 — was flying at an altitude of 25,000 feet southbound over the Caribbean Sea, approaching the north east point of Jamaica, when it went off radar, BBC reported.
The US had scrambled two fighter jets to investigate why the plane failed to respond to air traffic control from 10.00 a.m. local time (14:00 GMT).
Jamaican and US Coast Guard planes and ships were on their way to the scene till last report.
The plane went down about 14 miles (22 km) north-east of Port Antonio, said Major Basil Jarrett of the Jamaican Defence Force.
A North American air defence (Norad) spokesperson said it was not possible for the jet fighter pilots to see inside the plane before it crashed as the windows were frosted or fogged over.
A tweet from Norad suggested the pilot or pilots could be unresponsive due to “possible hypoxia” (a condition in which the body or a region of the body is deprived of adequate oxygen supply).