Emergency services were called to reports that a car containing five people had left the A38 dual carriageway at about 11pm on Saturday.
Derbyshire Police said a 36-year-old man and two women, aged 18 and 30, were declared dead at the scene.
A baby girl was taken to hospital and pronounced dead a short while later.
All four were passengers in the vehicle.
The driver, a 33-year-old man, was taken to hospital and treated for serious injuries. He has been arrested on suspicion of causing death by dangerous driving.
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