The collision happened on The Loaning in Motherwell, North Lanarkshire, at around 4.15pm on Tuesday.
Emergency services were called to the scene and the girl, named locally as Abbie Mclaren, was taken to Glasgow’s Royal Hospital for Children but later died.
Police said a 38-year-old man has been arrested and is due to appear at Hamilton Sheriff Court on Thursday.
Members of the community have launched a petition calling on North Lanarkshire Council to introduce traffic control measures on the road.
It states: “I can’t imagine the pain and suffering the family are going through at this tough time and I think we all would not want it to happen to anyone again.
“So even the simplest pedestrian crossing, priority system or even speed camera just to let children cross safely or at least slow traffic down could make it a lot safer for our children, grandchildren and even elderly.”
More than 8,700 people have signed the petition so far.
Motherwell & Wishaw MP Marion Fellows has also raised concerns about the situation and said she has written to North Lanarkshire Council to highlight the petition.
She tweeted: “My deepest condolences to the family and friends of Abbie who has sadly lost her life. My thanks go to the emergency services who attended and did their utmost to treat her.
“The community is rightly heartbroken over what has happened.
“I have since written to North Lanarkshire Council to raise the community’s petition with them and to join their calls in demanding action to improve safety on The Loaning and surrounding streets.
“I have particular concerns over speeding cars and safe crossings.”
A cousin of the schoolgirl has set up a GoFundMe page in her memory, which has raised more than £2,500.