Police said at around 9.30am this morning that they are at the scene outside Tesco in Piccadilly.
The area is currently cordoned off while officers examine the scene.
In a statement, North Yorkshire Police said: "We are at the scene of an incident in #York after a man was found injured outside Tesco in Piccadilly.
"Sadly he has since died.
"An investigation is underway to determine how he came to be injured.
"The area is currently cordoned off while officers examine the scene."
No details about his name or age have been released yet.