Officials indicated that at least 16 of the cases involved people of the same social group.
Officials indicated that at least 16 of the cases involved people of the same social group, with local media saying most belonged to the Orthodox Jewish community.
"We can say that the outbreak has largely been limited to unvaccinated people in a single social group and the disease is spreading among personal contacts in the group," Jeffrey Gunzenhauser, interim health officer at the LA County Department of Health, told AFP.
"There have been no infections spreading in the general community."
The outbreak of the highly contagious virus comes six months after California's strict vaccine law went into effect. A measles outbreak that originated at Disneyland in 2014 sickened 145 people across the United States and dozens more in Canada and Mexico.
That episode led to the new law in California that requires that all children be vaccinated unless a doctor submits an exemption for medical reasons. Personal and religious belief exemptions are not allowed under the new law.
Gunzenhauser said the new outbreak of measles is affecting individuals older than 12 years old, who would not be directly concerned by the new law.
He said the first person was diagnosed in early December and 16 more cases were reported in the last three weeks of 2016. The last case was diagnosed last week.
Measles is a highly contagious virus that lives in the nose and throat of an infected person, and can linger in the air for hours, according to the US Centers for Disease Control and Prevention.
Symptoms include a rash, white bumps inside the cheeks, a fever, runny nose and cough.
Severe complications can occur, leading to miscarriage as well as the risk of death by pneumonia or brain swelling.