Couillard, a neurosurgeon, made the comments Friday after health authorities confirmed this week that 10 Quebecers infected with the virus had not been vaccinated.
All 10 cases are clustered in the Lanaudiere region, northeast of Montreal, and are linked to the California Disneyland outbreak.
He pleaded with Quebec parents to recognize the science behind vaccines.
"The message that we have to send Quebec parents is one of responsibility," Couillard said in Montreal. "Listen, we are on very solid scientific footing here when it comes to vaccinations."
Couillard added "the truth of vaccination is a huge progress in our society. Why don't we have polio anymore do you think?"
Couillard encouraged families to vaccinate their children, but said the government cannot force people to do so because the courts recognize the right to refuse medical treatment.
"I recognize that courts have told us you cannot make it compulsory," Couillard said. "But on the other hand, I don't find it responsible for a parent not to follow the recommended immunization schedule."
More than 70 people in California and about two dozen others in six states, Mexico and Canada have been sickened in the outbreak that reportedly began after infected people visited Disney's California theme park days before Christmas.
While measles was declared eliminated from the U.S. in 2000, the illness has reappeared in recent years, brought in from overseas and transmitted to Americans and Canadians who didn't get vaccinated.
Authorities said Quebec's 10 cases are tied to the Disneyland outbreak.
Couillard said for the majority of people infected with measles, the virus is benign.
But in some cases the virus causes serious brain complications that are particularly damaging to children.
"As someone who has seen measles victims with serious complications, I cannot understand how we would want to expose ourselves to that, that we would want to expose our children to that," Couillard said.