A driver who allegedly struck a young boy with her vehicle outside a primary school in Sydney's south-west before driving away without helping the child has been arrested and charged by police.

The 32-year-old woman will face Campbelltown Local Court on Thursday following the crash outside Campbelltown East Public School on Monday afternoon, which left the seven-year-old boy with a leg injury.

Police will allege in court that the boy had left the school about 3pm on Monday and was attempting to cross Valley Road when the woman hit the boy in her red Mitsubishi Mirage hatchback.

The woman allegedly stopped briefly after the crash, before saying she was going to park her car up the road. Police allege the woman then drove away from the crash scene without helping the boy.

NSW Ambulance paramedics treated the boy before taking him to Campbelltown Hospital with a minor leg injury. He is expected to make a full recovery.