Fourteen people, including several children, were injured when a minibus crashed down an 8ft (2.4m) embankment.
The Ford Transit minibus is thought to have been carrying 15 people when it left the A629, between Wortley and Chapeltown, near Sheffield, on Sunday.
Police said four people suffered serious spinal injuries but none of the injured passengers is thought to be in a life-threatening condition.
One male passenger was arrested on Monday and later released on bail.
The A629 was blocked for several hours after the crash, at 1840 BST.
Police are appealing for witnesses to come forward.
Insp Jeff Young of South Yorkshire Police said: "This could have been a lot more serious than it actually was.
"It is still a serious collision and we have got a person still in hospital who has got serious head and internal injuries."
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