A person with the highly contagious infection visited the Southern California theme park between 9:15 a.m. and 8:35 p.m., the Los Angeles County Department of Public Health said in a news release.
The person also visited a Starbucks on South Sepulveda Blvd. in Los Angeles earlier on Oct. 16, between 7:50 a.m. and 10 a.m.
The agency said people who may have been at the Starbucks or Disneyland during those times are urged to contact their doctor if they have not been vaccinated, or if they are pregnant or have a weakened immune system.
Parents are also encouraged to alert a health care provider if their child or infant may have been exposed.
Symptoms, including a rash, can develop seven to 21 days after being exposed to measles, the agency said.
“For those who are not protected, measles is a highly contagious and potentially severe disease that initially causes fever, cough, red, watery eyes, and, finally, a rash,” a Los Angeles County health officer said in a statement.
The measles virus can easily spread through coughing and sneezing and can live for up to two hours in air where the infected person coughed or sneezed, according to the Centers for Disease Control and Prevention.
Other people can become sick if they breathe the contaminated air or touch a surface that has been infected with the virus and then touch their noses, mouths or eyes.
There have been 19 measles cases among Los Angeles County residents this year and another 11 cases involving nonresidents traveling through the area, the county health department said.
Measles can be prevented with the MMR (measles, mumps and rubella) vaccine, which is typically given in two doses during childhood. The CDC said both doses are about 97 percent effective at preventing measles and a single dose is about 93 percent effective.
NBC News reached out to Disneyland for comment and did not immediately hear back.