Emergency services were called to Leeds Road in Bradford city centre at about 1.55pm today following a report of a crash involving a pedestrian and a white VW Golf outside Debenhams, which is part of The Broadway centre.
The pedestrian, a woman in her 50s, suffered fatal injuries and was pronounced dead at the scene.
A 30-year-old man has been arrested in connection with the collision and is in police custody.
Sergeant Ann Drury of the Major Collision Enquiry Team, said: "Investigations are ongoing into this fatal collision and we are appealing for any witnesses who saw either the collision or the white VW Golf involved in the moments before the incident took place.
"Any witnesses or anyone who has information is asked to contact the Major Collision Enquiry Team on 101 referencing police log 0912 of 20/9."