The incident happened at about 11:30 a.m. Sunday at the intersection of 80th Street and Western Avenue.
Lisa Caesar and her 17-year-old son Marcus Walker were getting ready to return home to Sacramento after a family beach party.
The pair had run into a liquor store at the corner of that intersection to get a bottle of water.
Investigators said the suspect was going northbound on Western Avenue. The mother and son had just started to cross the street in the crosswalk when the car slammed into them.
The Los Angeles Police Department released surveillance video of the incident on Tuesday. The footage shows the 45-year-old woman and her son walking along a crosswalk. The video has been frozen before the point of impact. The disturbing scene was captured by a nearby surveillance camera.
Police said the car rammed into the victims and then drove off without stopping to help.
"When you leave a human being lying in the street, especially with her son standing over her, when you leave her like an animal, that I cannot understand," said Regina Caesar, Lisa Caesar's sister.
Authorities said the mother and son were rushed to an area hospital. Walker only sustained a sprained wrist, but his mother remained in critical condition with bleeding in the brain, a broken pelvis and ribs. She was recovering at the California Hospital Medical Center in downtown L.A.
"He's 17-years-old and he has mental disabilities. To leave a baby, standing in the street over his mother, is a horrible, horrible thing," said Regina Caesar.
Police describe the suspect as an African American woman in her mid 50s, about 5 feet 7 inches tall and weighing 160 pounds. Her vehicle is described as a dark, late-model car with possible front-end damage and a missing right mirror.
Caesar's family said they can't believe the suspect hasn't turned herself in.
"I did not expect to beg that person to come forward and do the right thing," said Regina Caesar.
If you have any information regarding this incident, you're urged to contact the LAPD at (877) LAPD-24-7 or (877) 527-3247.