The incident happened around 9 p.m. outside of 471 Lyons Avenue.
Police say the shots were fired after the girl's mother got into an argument with a Pathmark employee.
The girl was hit in the hand. She and another person who was struck, who is not believed to be the child's mother or a Pathmark employee, were taken in stable condition to University Hospital and are expected to be okay.
According to Mayor Wayne Smith, the argument included the employee was hit by a bag of seafood. That employee then called some friends, who showed up at the store and confronted the customer outside.
Words were exchange, guns were drawn and at least four shots were fired. Four shell casings were found outside the store.
No arrests were immediately made.
There were several other shoppers in the store when the shooting happened, and the store was locked down for a short time.