The aircraft, a Four Winds 192 made in July, was flying north before making a sharp turn southeast and crashing, said Alan Yurman, spokesman for the National Transportation Safety Board.
Witnesses did not report seeing smoke from the engine, he said.
"One of the witnesses said they saw it at about 500 feet and it was wobbly," said Alan Yurman. The pilot, who was the only one aboard, has not been identified, Yurman said.
The FBI was keeping in close contact with investigators, said FBI Miami spokeswoman Judy Orihuela.