"They had it as children, they were miserable for a few days, and they all turned out fine," Bevin said in an interview with WKCT, and a Bowling Green radio station.
Bevin and his wife, Glenna, have nine children between the ages of 5 and 16, according to his campaign website.
The governor says he supports parents who choose to get their children vaccinated and also those who refuse to do Sat. But he said the decision would not be up to the government.
"This is America," he said. "
CNN has reached out to Bevin for comment
There have been 32 cases of chickenpox reported.
The teen and his father allege that he is being discriminated against because of religious beliefs. Some Catholics worry about vaccines derived from cell lines associated with abortion.
The Northern Kentucky Health Department argued the ban was an appropriate and necessary response to prevent further spread of this contagious disease.
Chickenpox has not been dispensed since the vaccine was introduced in the United States in 1995, but each year more than 3.5 million cases are prevented by chickenpox vaccination, the CDC said.
Initially, only one dose of vaccine was recommended for children. But when experts realized that a small percentage of children did not mount robust immunity after the first dose, the recommendations were changed. The two-dose vaccination program has resulted in a smaller number of outbreaks, according to the CDC
CNN's Madison Park has contributed to this report