The incident occurred at 3.45pm on the Pestalozzistrasse in the centre of the city, cantonal police said.
The child died from the injuries sustained after being transported to hospital by ambulance, accompanied by an emergency team.
A 37-year-old van driver had unloaded goods for a commercial business and drove over the girl without seeing her as he pulled out, police said.
The owner of a Turkish store, Elan Kugathasan, who witnessed the accident, said the child was playing near the vehicle.
“The girl was playing in front of the store near the vegetable stand,” Kugathasan told the 20 Minuten newspaper.
He said the child’s parents were a bit further away.
“Then the van drove off and rolled over the child.”
Kugathasan said the mother and the father both “collapsed” after the accident.
“The woman was on the ground,” said the store owner, who knew the family well.
A care team dispatched to the scene looked after the parents.
Police, meanwhile, have launched an investigation into the actions of the driver.