Federal Aviation Administration spokeswoman Kathleen Bergen says the Socata TB10 went down in Shirley around noon, shortly after taking off from nearby Brookhaven Calabro Airport.
Suffolk County police say one person has died, and two others have been taken to Stony Brook University Medical Center with burns.
Their conditions aren't immediately available. The names of the people in the plane haven't been released. It's not immediately clear whether the pilot is among the injured.
The Socata TB10 - a model known as the "Tobago" - is a single-engine propeller plane.
Witnesses say neighbors tried to douse the flames with fire extinguishers and garden hoses.