Los Angeles police said they responded to the shooting shortly before 2:30 p.m. in the 900 block of N. Oxford Avenue, where the victim was discovered unconscious and not breathing.
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Video from AIR7 HD showed a sheet covering the woman's body in the driveway to the apartment complex.
Family members later identified the victim as 27-year-old Cindy Yaneth Lopez Velasquez. Authorities said she was walking to the apartment complex with friends when she was shot.
Family members say they were about to take a trip to the mall and don't know who would target her.
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The suspect, who police said used a handgun, was last seen going northbound on Oxford Avenue. It was initially believed he was in a Toyota Rav4, but now they believe he may have took off running.
"It appears the victim had walked to this location and was maybe followed by the suspect," said Lt. John Radtke of the LAPD.
Police are combing neighborhood surveillance video looking for clues as they search for the gunman.
Police said Velasquez was followed when she was shot by the suspect. It's unclear how the two knew each other but investigators do not believe the shooting was random.
Family members said Velasquez was studying criminal justice and working to become a lawyer to help people in her community. They said the victim did not have a boyfriend, but police are not ruling anything out.
Loved ones were gathered at the scene, mourning the young woman's death.
Many of the woman's Guatemalan family members live across the street from where she was gunned down.
"She's one of a kind. One of a kind young lady," said Yolanda Mackler, the victim's aunt. "We are so devastated."