The 40-year-old Californian, Vicki Cruse, was performing in a light aircraft when it plummeted to the ground.
The woman, who was flying alone, was pronounced dead at the scene.
No one else was injured.
The Edge E40 came down in the south-west corner of the racing circuit.
A police spokeswoman said: "Thames Valley Police is currently at the scene of an aircraft crash at Silverstone, Dadford Road, Buckingham.
"Police were notified at 12.12pm that a single aircraft taking part in an acrobatic show at Silverstone had come down on the circuit."
The Air Accidents Investigation Branch (AAIB) is investigating.
The World Aerobatic Championships website states the event is held every two years and brings together the "best aerobatic pilots in the world".
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