No cases have been reported yet, according to the California Department of Public Health, but local health agencies have warned it can take up to 21 days for symptoms to appear.
"Measles is spread by air and by direct contact even before you know you have it," Dr Muntu Davis, Los Angeles County’s health officer, said.
The girl had measles when she arrived at Los Angeles International Airport on 11 August and has since returned to New Zealand, officials said.
She is thought to have gone to Universal Studios, the TCL Chinese Theatre and Madame Tussauds in Hollywood, and the Santa Monica beach and pier on 14-15 August after going to Disneyland, authorities said.
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Dr Nichole Quick, Orange County's health care officer, urged anyone who has symptoms to call a health provider before going to the doctor to avoid additional exposures.
She added that more measles cases from international travellers were expected generally in California, due to an increase in the illness overseas.
"We're in general concerned with the outbreaks going on in places in this country as well as internationally," Ms Quick said.
Disneyland officials said on Friday that no employees at the theme park had reported contracting the illness and the risk to employees and visitors is “likely low”.
"We maintain rigorous sanitation standards to protect guests and cast, and earlier this year we strengthened our immunisation programme and educational resources for cast members," a Disneyland statement said.
The United States in currently dealing with its worst outbreak of measles in decades, with more than 1,200 cases reported across 30 states since October 2018, according to the US Centres for Disease Control and Prevention (CDC).
Globally, the number of cases of measles has nearly tripled during the first seven months of 2019 compared with the same period last year, the World Health Organisation reported this month.
Although the disease was declared eliminated in the US in 2000, CDC officials have said the country risks losing that status if the current outbreak, which began in October 2018 in New York, continues until October 2019.
Measles, which can sometimes cause death, is considered one of the most contagious diseases in the world and infects 90 per cent of people who are not immunised to it, according to the Los Angeles County Health Department
Its symptoms include fever, coughing, red eyes and a characteristic rash which can appear up to three weeks after exposure.
Agencies contributed to this report