"If you were to look at Disneyland, the quarter that we're currently in, we're up from where we were last year in both attendance and in bookings, or in reservations," Iger said in an interview with "Closing Bell."
"We just haven't seen an impact."
The outbreak began in December at the California amusement park and has now spread to several other states. According to the Centers for Disease Control and Prevention, 102 people from 14 states reported coming down with the disease in January and most of those cases were part of the outbreak linked to Disneyland.
Iger said it would be smart for parents of young children to use caution when going to public places. The measles vaccine is typically given to children when they turn 1 year old.
"This is a time for parents ... with kids under the vaccination or inoculation age to be cautious taking their kids to public places, not just theme parks, there are a number of other places: mass transportation, movie theaters, you can probably name a number of them," he said.
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That said, Iger noted that the percentage of visitors to the Disney parks with children that young is not particularly large.
While professing he's no expert on vaccinations, Iger said he would personally advise it in light of the research he's seen.
"It's a proven strategy in terms of combating a disease that could be dangerous to young children."