The four-by-four, which was carrying four people from Marple, left the Roych bridleway, off Sheffield Road, and overturned at about 6.15pm on the Roych.
Three casualties escaped with minor injuries and were treated by East Midlands Ambulance Service.
Derbyshire, Leicestershire and Rutland Air Ambulance were called out to help with the one remaining patient, who was still trapped in the vehicle.
The patient was extricated from the vehicle by the fire and rescue service. She was then immobilised and flown to University Hospital of North Staffordshire for further treatment.
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Her current condition is unknown.