Linda Carson, 44, was with her pet terrier Buster on Sunday evening when a silver Ford Mondeo mounted the pavement and struck her.
The mum-of-one was just a few hundred yards from her home in Motherwell, when the incident happened at 8.10pm.
Her husband Robert, 47, rushed to the scene after he was contacted by a witness who retrieved his phone number from the dog’s collar.
He comforted his wife but she was pronounced dead at the scene when emergency services arrived. It is believed her dog survived the incident.
The car struck Linda on Muirhouse Road while travelling round a bend before crashing into brick pillars at the entrance to a tower block.
Witnesses said the driver of the car got out and ran away following the crash as residents rushed to help. Police are believed to be following a positive line of inquiry.
Tributes have been paid to Linda by friends and neighbours.
Her husband and daughter were being comforted by relatives at their home yesterday and did not wish to comment.
A family friend said: “Everyone is just absolutely devastated at what happened, we can’t believe it.
“Linda was such a lovely person and we are just shattered that she has gone. She was just out walking her dog on Sunday evening as she did every day when this happened.
“We don’t know all the details of what exactly happened but the police are keeping the family informed.
“One of the people who went to help Linda contacted Robert because the number was on the dog’s collar.
“He went up to the scene but there was nothing that could be done for her.”
Another neighbour said: “She doted on her dog Buster and I would see her out walking him every day.
“She was a very nice lady and my heart just goes out to the family.
“Her husband and daughter will be devastated.”
Police Scotland have appealed for witnesses to the crash.
Sergeant John Tait, from Motherwell Road Policing Unit, said: “We are appealing for anyone who was in the area around the time of the incident and saw what happened to get in touch.
“Anyone with information can contact police on 101.”