The California Safely Surrendered Baby Law was passed in 2001 to prevent the death of newborns abandoned by their parents.
The woman asked the man if he could take her child, deputies said.
Fuentes described the "awful, chilling, moment" he was approaching a customer's house in his vehicle and saw something white moving in the road, which he initially thought was an animal.
A stricken mother begged strangers to take her newborn baby - then dumped the girl in the middle of a freezing road with her umbilical cord still attached.
The CHP says the infant was dressed in a soiled onesie in 30-degree weather.
KFSN-TV reports the hours-old baby was wearing only a onesie when a newspaper carrier found her before dawn Monday on the center line of the road in Madera County. "OK, you know, this is a baby".
Aurelio Fuentes Jr. told abc30: 'I see a bright white thing laying on the road I'm like is this an animal.
He immediately called 911 and waited with the baby until an ambulance arrived, fearful the little girl might be taken by the coyotes common to the area. Ironically, there was a staffed fire station within a mile or two, and Valley Children's Hospital is very nearby.
Now authorities are on the hunt for the baby's mother.
Investigators are looking for a Hispanic female, likely in her early 20s, who left the scene in a small white SUV.
The baby was taken to the nearest hospital and is expected to make a full recovery. "We'd like to remind everyone that there are many safe surrender sites that will allow someone to surrender a newborn child without any questions asked".
One eyewitness reportedly saw the mother and told police she appeared so desperate to get rid of her baby girl that she was driving around Madera Ranchos, California early Monday morning asking people to take the newborn.