The twin-engine Light Aircraft came down at about 14:20 BST
The pilot was uninjured but the co-pilot was taken to the John Radcliffe Hospital with minor injuries.
Aircraft struck the farm building near Enstone Airfield causes barn fire killing several chickens.
Six fire engines are at the scene as crews battle the blaze.
The Air Accidents Investigation Branch is at the site of crash.
Gill McNeil, an instructor who witnessed the crash, said it was “remarkable” the injuries had not been worse.
Describing the collision, she said the plane “turned very, very sharply towards the airfield in a steep dive with the wings rocking, and then crashed into the barn behind us”.
She added: “It all happened very quickly.”