The incident happened on Wednesday in Calne when a van was involved in a collision with the child.
Town mayor Robert Merrick is a family friend and could not contain his grief as he explained the shock and disbelief the family were going through.
“Words just fail me,’” he said. “The family are so shocked and it is unbelievable that the town of Calne has had yet another awful tragedy.”
He explained he had got to know a family member on moving to Calne over 20 years ago.
“This is another tragedy for Calne, and so devastating for a family to lose such a young child.”
On our sister paper the Gazette & Herald's Facebook page, readers paid tribute.
Sarah Rice-Wilford said: "This is just heart breaking. Thoughts are with the family xx."
Sven Bartram added: "Dreadfully sad."
Police released a statement after the incident.
They said: “Officers were called to Campion Close shortly after 12pm after a crash between a van and a pedestrian.
"The little girl died at the scene and her family was supported by specially-trained officers."
The van driver stayed at the scene and is helping police with their inquiries.
Insp James Brain added: “This is a tragic incident and our thoughts are with the girl’s family at this incredibly difficult time.
“I ask that their privacy is respected and we will also be working with the local community who would have no doubt been impacted by this.
“We understand that people will want to pay their respects and come together at this difficult time, but can we please ensure this is done safely and to keep in mind the current Government guidelines regarding Covid restrictions and maintain social distancing.
“Our investigation into the circumstances surrounding the incident is at a very early stage and we won’t be providing any further update at the moment.”