Police have charged a man with 41 offences over a hit-and-run which left a woman and seven children injured in Melbourne's south-east last week.

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.

He has been charged with offences including theft of motor vehicle, speed in a manner dangerous, reckless conduct causing serious injury, fail to render assistance and unlicensed driving.

Police said he has been remanded to appear in Melbourne Magistrates' Court court on Tuesday.

Detective Senior Sergeant Melissa Nixon said the man was known to police.

"Fortunately for us, we had some dashcam footage and that assisted us in our investigation … it was just a matter of time and resources — we put everything into it, and located him."

She said the ute involved in the incident was stolen from Clyde in February.

On Friday, 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.

Senior Sergeant Nixon said the dashcam footage of the incident was "confronting" viewing.

"As you would've seen in the aftermath of what occurred, it's pretty distressing for some young children and family members to see what happened," she said.