Officer Simon Drobik said the man, who was initially hospitalized in critical condition, was taken off life support sometime in the past 24 hours.
Drobik did not identify the man.
Officers responded to the Flying J truck stop, near 98th and Interstate 40, around 8 p.m. following reports that someone had been run over.
Police found a man severely injured and the suspect had fled the scene.
Investigators released surveillance photos of the suspect inside the store and the car he left the scene in, a silver Chevrolet Cobalt car with a Pennsylvania license plate.
The city has seen 19 homicides so far this year, with five resulting in arrests.