The plane went down about 8:30 EDT, shortly after taking off from Brighton Airport, which has been shut down until the Federal Aviation Administration completes its investigation of the crash, the Detroit Free Press reported.
The passenger who was killed was described only as a female visitor from Costa Rica.
The pilot -- who was hospitalized for treatment of extensive injuries -- is a man in his 70s who owned the plane, the newspaper reported. Brighton Airport Manager Bill Bertrand said the man had been flying for 30 or 40 years.
The names of the victims have not been released.
Bertrand said there was no distress call from the plane before it crashed.
Investigators from the FAA and the National Transportation Safety Board were at the scene of the crash, along with state and local fire and law enforcement officials, the Free Press said.