Police said the boy was visiting Bay View Nursery and Garden Centre, Bolton-le-Sands with his mother on Thursday, April 30.
At between 2pm to 2.15pm, it is thought that the boy ran out from the back of two parked cars and was knocked by a separate passing car.
The boy suffered a broken leg as a result.
Road policing officer PC Michael Taylor said: “We are trying to find the owner of the car that has hit this young boy and appeal for them to come forward.
“At this stage, we aren’t sure whether the driver even knew that they had hit him; it could be that they were unaware.
“If you have any information at all about this incident, I would ask that you get in contact with us.”
The car involved is described as a small, possibly brown or beige, bubble-shaped vehicle.
Anyone with any information can contact PC Taylor on 101 quoting log number LC-20150430-099.
Alternatively, they can contact Crimestoppers anonymously on 0800 555 111 or online at Crimestoppers-uk.org.
No personal details are taken, information is not traced or recorded and you will not go to court.