Candice Boezak, 28, from Rocklands in Mitchells Plain was mowed down by a car on Friday just before 7pm on Baden Powell Drive.
Candice had been living under a bridge on the road with her boyfriend.
Her 60-year-old mother, who asked not be named, said: “We are appealing for witnesses to speak out if they saw or know about this incident.
“She was our only child and she has a 10-year-old daughter who is very hurt by what happened to her mommy.
“I last saw her Friday morning. She came in here and was very happy.”
Their neighbour and Rocklands Neighbourhood Watch controller, Valerie Moses, 67, was on the scene on Friday.
“Candice had a gush on her forehead and was wearing a tights and long-sleeved top.
“She lived under the bridge on Baden Powell Drive and didn’t deserve to be killed this way.
“When I got there, the road was closed off for cars and her body was lying in the middle of the road.
“A broken part of a number plate with only ‘CA’ on it was lying close to her body. Parts of a car’s bumper were also there.
“Her boyfriend arrived at the scene later and asked me if she was still wearing her tights.”
Police spokesman Lieutenant-Colonel Andrè Traut says: “The driver of the [silver] VW Polo which we believe struck the victim, fled from the scene and is yet to be arrested.
“Police are investigating a culpable homicide.”
* Anyone with information can call police at Crime Stop 0800 10111 or 021 377 5000.