"We can confirm that the aircraft was a military aircraft," said a spokesman from Cambridgeshire Police in south east England.
"There is believed to have been one person on board, and there has been one confirmed fatality."
The US Navy single-seat F/A-18 Hornet had taken off from RAF Lakenheath airforce base in Suffolk but was not reported to be linked to the facility.
Cambridgeshire Fire and Rescue Service said they were called just after 10.30 am (1500 IST).
"We were called following reports of an aircraft crash at Redmere," said a spokesman.
Amateur aviation enthusiast Roger Smith told the BBC that the plane was part of the Hornet Marine Corps and was flying back to the US from the Middle East having arrived at Lakenheath over the weekend.
It is the third recent incident involving the base, which hosts the US airforce's 48th Fighter Wing.
One of its F-15 fighter jets crashed into a field last October. The pilot in that incident successfully ejected and escaped without serious injury.
In January 2014, four airmen were killed in Suffolk when a US helicopter crashed while flying low on a training exercise.
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