One expert says the infections of fully vaccinated people show the need for "herd immunity."
Dr. William Schaffner, an infectious disease expert at Vanderbilt University Medical Center, said herd immunity is important because no vaccine can perfectly protect 100 percent of people.
"If everyone else is vaccinated, then the weak are protected, because they are surrounded with a cocoon of protection of others," Schaffner said. "The herd of strong protect the few weak."
However, measles is one of the most infectious viruses in existence. It will infect 90 percent of susceptible people if they are exposed. The airborne virus can also remain in the air for hours, infecting people if they are in the same vicinity as someone who is ill. For every person who gets it, the virus can spread to 18 other people.
Schaffner said the fact that even a few people who were vaccinated have become infected shows how many people have been exposed to the virus.
"For every person who's vaccinated who comes down with measles you can assume that between 40 to 80 people who were exposed," said Schaffner.
The measles virus was declared eradicated from the U.S. in 2000 and reached an all time low with 37 cases in 2004. However, cases of the virus have started to increase due to "clusters" of unvaccinated people and increased international travel. Last year 644 people were infected with the disease in the U.S.
ABC News' Liz Neporent, Sydney Lupkin and Dr. Richard Besser contributed to this article.