Officers responded to the intersection of 65th Street and Elmwood Avenue, just outside Lene Daily Child Care.
The child was rushed to Children's Hospital of Philadelphia and later listed in stable condition.
"It sounded like two cars collided, and then all of a sudden people started running," one witness recalled.
Investigators believe a silver SUV was involved in the incident.
Anyone with information is urged to contact police at 215-686-TIPS.