The unnamed 74-year-old victim was found in Coronation Street, in the Pear Tree area, just after 05:00 BST on Thursday, Derbyshire Police said.
He died several hours later and a post-mortem examination showed he had suffered head and chest injuries consistent with being hit by a vehicle.
Officers are trying to trace a dark hatchback car seen in the area.
Detectives said they were particularly interested in speaking to anyone who was in the area of Coronation Street, Princes Street, Holcombe Street or Harrington Street between 04:00-05:00 BST on Thursday or anyone who saw a collision.
They are also asking local garage owners to get in touch if anyone has brought a damaged car in for repair.
A man who was found with fatal injuries in a Derby street may have been hit by a car which did not stop.