The shootings occurred in the early morning hours of Sunday, Monday and Wednesday, officials say.
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According to LAPD Chief Michel Moore, the three victims of the shootings, all men ranging between 37 and 62 years old, were killed as they slept alone in generally open areas.
WATCH: LAPD Chief speaks on 'commonalities' of killings of homeless men in LA
LAPD Chief speaks on 'commonalities' of killings of homeless men in LA
"Each of the victims were in an open area, whether it be a sidewalk or an alley, they were alone, and from other information that we've gathered at this point, we believe a single individual approached each one and shot and killed each one as they slept," said Moore during a Friday afternoon press conference.
The first killing occurred around 3 a.m. Sunday in an alley near the intersection of 110th Street and Vermont Avenue in South L.A., police said. The victim was identified as Jose Bolanos, 37.
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The next day, Mark Diggs, 62, was shot and killed at about 5 a.m. in the 600 block of Mateo Street in the downtown area.
The third fatal shooting happened around 2:30 a.m. Wednesday near the intersection of Avenue 18 and Pasadena Avenue in the Lincoln Heights area, where the body of a 52-year-old man was found.
Though police did not release a detailed description of the suspect, they released an image from surveillance footage showing the person they believe may be linked to crimes. They also released a photo of a possible vehicle involved.
Mayor Karen Bass urged people living on the streets to seek shelter and asked them not to sleep outside as the search for the suspect continues.
"This news is devastating to our city," said Bass. "Living in the streets, we already know, is dangerous, and we already know that four to five people die on our streets from a range of causes, and violence is certainly one of them. I want to be very clear about what we're facing today. This is a killer who is preying on the unhoused, and as always, like we do in the face of an emergency, here we are again."
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In response to the manhunt, a winter shelter program was activated to provide additional safety for unhoused individuals. The Los Angeles Homeless Services Authority in a statement announced its Augmented Winter Shelter Program will be available through Monday night.
Anyone with information is urged to contact LAPD's Robbery-Homicide Division, Homicide Special Section, at 213-486-6890. You can always call the LA Regional Crime Stoppers at 1-800-222-TIPS (800-222-8477) or visit www.lacrimestoppers.org.
City News Service, Inc. contributed to this report.