The eight pedestrians were struck by a utility at an intersection on the Princes Highway at Pakenham at 3:30pm on Friday afternoon.
Police said the driver fled the scene on foot before they arrived, leaving the vehicle behind.
A 21-year-old man was arrested at a house in Pakenham on Monday afternoon and is helping police with their inquiries.
Ambulance Victoria said a woman aged in her 30s had chest, back and shoulder injuries and was taken to The Alfred hospital in a serious condition after the hit-and run.
The seven injured children were all primary school aged.
One girl had abdominal and leg injuries and was taken to the Royal Children’s Hospital in a stable condition.
Paramedics said five other girls had cuts and grazes.
Three were taken to Dandenong Hospital and two were transported to the Monash Medical Centre.
A boy was treated at the scene but was not taken to hospital.
