WHITESBURG, Ky.—As Congress works to repeal President Barack Obama’s signature health law, Kentucky Republican Gov. Matt Bevin is already at work unwinding some of its provisions in his state.

Mr. Bevin has dismantled the state’s health-insurance exchange, moving patients to the federal website last year. He has proposed introducing new conditions for recipients of Medicaid, the federal-state health program for the poor, that would require patients to pay premiums of up to $15 a month and perform employment-related or community-service activities, among other provisions.

His administration is waiting for the federal Centers for Medicare and Medicaid Services to decide whether to approve the plan. The agency’s new head, Seema Verma, helped craft Kentucky’s proposal, but said she would recuse herself from the decision-making process.

The plan is “designed to improve people’s health, education and employment opportunities, while stabilizing the high costs of providing care to our most vulnerable citizens,” said Doug Hogan, a spokesman for the Kentucky Cabinet for Health and Family Services.

It is a reversal for a state whose health-insurance exchange was hailed as a model of success when the federal marketplace and some state ones were faltering.