Children in Hebden Bridge took pictures as a black BMW hit the 19-year-old girl as she waited at a bus stop with friends.
The incident happened at 5pm last night outside Calder Holmes Park, New Road, Hebden Bridge.
The driver of the car mounted the pavement and struck the girl, who has not been named.
A police helicopter, video vans and an ambulance were called. One man was arrested and is in custody. Another four were arrested after spray-painting a police car at the scene.
The girl suffered cut legs and bruising. She was taken to Calderdale Royal Hospital but later released.
One teenager filmed the incident on his mobile phone. It is believed others may have captured the scene, too.
Inspector Colin Sanson said: "Police were called to Hebden Bridge where a vehicle had collided with a 19-year-old local girl.
"When police attended, graffiti was drawn on a police car. As a result, police arrested another four people.
"Some evidence was collected at the scene, but we are not in a position to go into detail."
The car involved had earlier been seen driving through red traffic lights.
A police spokesman said: "There were reports of incidents involving a black BMW in the Hebden Bridge area, including nearly running someone over in a bus lane. We believe the car may have been stolen."
A 12-year-old girl at the bus stop said: "The car went on the pavement and hit the girl. There was a lot of screaming."
Police are asking witnesses to call their helpdesk on 01422 337070.