North Yorkshire Police said the incident happened at the Littlethorpe supermarket at about 6.40pm on Saturday January 22 and involved a white utility van.
“The pedestrian, a man in his 40’s, sustained an injury as a result of the incident and is receiving treatment at hospital,” said a force spokesman.
“The van did not stop at the scene and so we are appealing for information to help identify the vehicle and its occupants.”
Anyone who was in the area of Morrisons between 6.20pm and 6.50pm and has any dashcam or video footage, is asked to contact police.
Dial 101, press 1 and pass information to the Force Control Room, quoting reference number 12220012344.