Police Superintendent Stephen Dean said the single-engine plane crashed in waters a few miles (kilometers) off Grand Bahama island and all four people aboard were killed.
"All are believed to be Americans. It is thought they were on some kind of sightseeing tour," Dean said.
Emrick Seymour, assistant police commissioner for Grand Bahama, said the Cirrus 22 plane crashed minutes after takeoff from the island's international airport. He said the pilot radioed that the plane was "experiencing some engine problems."
A statement from the Royal Bahamas Police Force said the aircraft was destroyed.
Information about the victims' identities was not immediately provided by Bahamian authorities. Seymour said police were "right in the middle of the investigation."