According to the California Department of Public Health website, 52 of those cases are linked to an outbreak at Disneyland.
There are four confirmed cases in Riverside County, where the Desert Sands Unified School District told 66 students -- who have either not been vaccinated for measles or can't show proof -- that they need to stay home.
CNN affiliate KESQ reported
that one student at Palm Desert High School is suspected of having had measles. The student has been cleared to return to class but health officials are still trying to determine if the student actually had measles.
For now, the others will have to study at their homes.
"They are going to be asked to stay home until the incubation period for contagion is complete," a spokeswoman for the school district, Mary Perry, said of the students who were released. The earliest a student can return without proof of vaccination is February 9, the station reported.
Of the 79 California cases, 15 are in Los Angeles County, and all victims were unvaccinated for measles, said Dr. Jeffrey Gunzenhauser, the county's interim health officer.
Of those 15 county cases, 14 are linked to Disneyland, Gunzenhauser said.
"In L.A. County, we're, fortunately, highly vaccinated. Five percent or less are unvaccinated," Gunzenhauser said.
There are 16 cases linked to Disneyland outside California (seven in Arizona, three in Utah, two in Washington, one in Colorado, one in Oregon, one in Nebraska and one in Mexico).
Arizona officials said they have identified 1,000 contacts of the seven cases in their states. They're asking anyone within that group to isolate themselves for 21 days if he or she isn't vaccinated.
The disease outbreak became apparent when visitors reported coming down with measles after visiting the park from December 15 to December 20. At least five Disney employees have been diagnosed with measles, Disney said.
Also, the families of 195 children in Mesa, Arizona, have been contacted because they were in an urgent care clinic with someone who has measles.
Midway across the country, at the University of Minnesota, a student who had traveled abroad is self-isolating after contracting the disease, the school said in a statement
. The university is working to find everyone who may have been exposed to the student, who attended class four days last week.
Though students have largely been immunized because of enrollment requirements, the university warned anyone who had not been vaccinated to be vigilant.
Minnesota is one of 27 states that reported measles cases last year, according to the Centers for Disease Control and Prevention
. The 644 cases reported in 2014 mark a stark spike compared with recent years. Since 2001, the number of cases has topped 100 only five times, and 2011 was the only year in which cases topped 200.
Measles is a highly communicable respiratory disease caused by a virus and spread through the air. Measles starts with a fever, runny nose, cough, red eyes and sore throat, the CDC says.