(Adds details from California Department of Public Health)

Jan 21 (Reuters) - Five employees of Disneyland have been infected with measles in an outbreak traced to the California amusement park, although three of them have recovered from the viral disease and are back on the job, company officials said on Wednesday.

Orange County health officials told the Disneyland resort on Tuesday that two employees had tested positive and had been placed on medical leave, the fifth case since last Thursday, a Disney spokeswoman said.

"Cast members who may have come in contact with those who were positive are being tested for the virus," Walt Disney Parks and Resorts Chief Medical Officer Dr. Pamela Hymel said in a statement.

California health officials earlier this month linked the worst outbreak of measles in more than a decade to Disneyland, saying anyone who visited the amusement park in Anaheim between Dec. 15 and 20 may have been exposed.

More than 50 people have become infected in California as well as other U.S. states and Mexico, health officials said.

Disneyland began offering vaccinations and medical screenings after it learned of the outbreak on Jan. 7, a spokeswoman said. Last Thursday, it learned one employee tested positive. Three have been treated and are back at work.

On Tuesday, Huntington Beach High School, about 15 miles (24 km) from Disneyland, told students who had not been vaccinated for measles to stay home for two weeks after learning one of their classmates was infected.

The California Department of Public Health said there have been 59 confirmed measles cases among California residents so far in 2015. Of those, 42 cases have been linked to exposure in December at Disneyland.

This includes the five employees, four of whom worked there and one who is believed to have been infected as a guest. Of the cases outside California linked to the Disneyland outbreak, there has been one in Mexico, three in Utah, two in Washington state, and one each in Oregon and Colorado.

Measles typically begins with fever, cough, runny nose and red eyes, followed by the appearance of a red rash that typically starts on the face and spreads downward. The sometimes deadly viral disease can spread very swiftly among unvaccinated children.

There is no specific treatment and most people recover within a few weeks. But in poor and malnourished children and people with reduced immunity, measles can cause serious complications including blindness, encephalitis, severe diarrhea, ear infection and pneumonia.

(Reporting by Eric M. Johnson in Seattle; Editing by Peter Cooney and Eric Walsh)