Yet while the city says it has done considerable outreach about the new rule, there has been some confusion among parents and schools.

At a meeting in early December between health officials and religious-school administrators, for example, some school leaders reported significant resistance from parents against the new regulation, in part because the parents said their children’s doctors were telling them the vaccine was unnecessary.

“There is going to have to be a learning curve,” said Deborah Zachai, director of education affairs at Agudath Israel of America, an ultra-Orthodox Jewish umbrella organization that was represented at the meeting. “I suspect that next year the doctors will be more aware of it, and the issue will be less prominent.”

In December, the city’s health board voted unanimously in favor of the flu vaccination rule, which does not apply to older children. There was minimal public discussion about the rule, which was overshadowed by other Bloomberg public health initiatives like the large soda ban. The public hearing before its passage was lightly attended, and many of the opponents who spoke were from organizations generally opposed to mandatory vaccination programs.

Among them was Kim Mack Rosenberg, the president of the New York metro chapter of the National Autism Association. She believes that vaccinations may contribute to autism, though no link has been proven.

“It is a requirement that is putting a burden on children and no one else,” she said this week. “Adults aren’t generally required to get the flu vaccine, and we are asking our most vulnerable children to get it.”

On rare occasions, flu vaccination can cause serious problems, such as severe allergic reactions. A report from the National Vaccine Injury Compensation Program states that there have been 1,633 claims of injury and 81 claims of death attributed to flu vaccines in all age groups since 2005, of which 924 have been compensated. But federal officials stress that such settlements are not an admission that the vaccine caused the injury.