Leslie Moran, a spokeswoman for the New York Health Plan Association, the trade association for most health plans across New York State, said the industry did not object to having to cover gender dysphoria.

But she said the industry was concerned that the governor’s order could raise costs in the new year that were not contemplated during the recent round of rate-setting. And she said companies were concerned that the policy would open the door for other services that people might seek, claiming they were medically necessary for mental health reasons.

“It sets a precedent,” Ms. Moran said.

Benjamin M. Lawsky, the state’s superintendent of financial services, which regulates insurance, said he would “be very surprised” if the change led to a noticeable rise in insurance premiums, because the number of transgender people would be such a small part of the insurance pool.

“It will further solidify the rights of a group that probably weren’t always being treated as equal to everybody else, and that’s sort of fundamental to our system,” Mr. Lawsky said.

The new policy comes as the state is trying to negotiate a settlement in a class-action lawsuit seeking Medicaid coverage for sex-change treatments, and advocates said they hoped it was a signal that the state was going to approve that coverage as well. Mr. Lawsky said that State Senator Brad Hoylman, a Manhattan Democrat, had brought the issue to his attention in June, by pointing out that several other states had barred insurance companies from excluding gender-change treatment.

At that time, a review board of the United States Department of Health and Human Services had just ruled that transgender people could no longer be automatically denied coverage for sex reassignment surgeries under Medicare, reversing a policy in place since 1981.

Mr. Hoylman said this week that he knew people who had had to scrape together money from fund-raisers to pay for their gender reassignment surgery. “Nobody should be in that position in order to embrace such a fundamental aspect of their personhood,” he said.