Four people — a baby girl, two women aged 18 and 30, and a 36-year-old man — died after a red Hyundai left the A38 in Derby and hit trees around 23:00 BST Saturday.
Derbyshire Police said the 33-year-old driver suffered serious injuries, remains in hospital and was arrested on suspicion of causing death by dangerous driving.
The crash happened between the A50 Toyota Island and the A516; the baby was taken to hospital but died shortly afterward, while the other three victims died at the scene.
All five people were from Leeds in West Yorkshire, police said, adding relatives have been informed and are being supported by specialist officers.
The dual carriageway was closed for several hours before reopening, and police are seeking witnesses and dashcam footage.