A police spokesman said: "Officers investigating the death of a man on Rother Way in Chesterfield, in the early hours of today, have arrested a suspect.
"A 41-year-old local woman contacted the police this morning and has been arrested on suspicion of causing death by dangerous driving. She’ll be questioned this afternoon.
"Thank you to everyone who has contacted the police as a result of the appeal.
"The road has been reopened.
Officers were called to the road shortly after 12.30am where a man had been found dead in the carriageway.
The man has not yet been formally identified but is thought to be 46-years-old and live locally. His family has been told.
Anyone who drove along the A619, near the Sainsbury’s store, between 11pm and 12.40am should contact the police on 101, quoting incident number 41/28/05/16.