Wisconsin’s Supreme Court on Wednesday rejected the extension of a stay-at-home order by Gov. Tony Evers, siding with Republicans in one of most high-profile challenges of its kind to the emergency authority of a statewide official during the coronavirus pandemic.

Mr. Evers, a Democrat, had extended the prohibition on most travel and operations of nonessential businesses until May 26.

But in a 4-to-3 ruling, the conservative-leaning court said that measure had exceeded the authority given to Wisconsin’s top health official under state law.

“An agency cannot confer on itself the power to dictate the lives of law-abiding individuals as comprehensively as the order does without reaching beyond the executive branch’s authority,” the justices wrote in the ruling.

There have been legal challenges to stay-at-home orders in Michigan, California, Kentucky and Illinois, but none of those were successful in persuading a court to fully strike down the order, as the plaintiffs in the Wisconsin case were.

The ruling, a spokeswoman for Mr. Evers said, appears to immediately end all provisions that have required Wisconsin residents to stay home.

“We’re definitely concerned,” the spokeswoman, Melissa Baldauff, said of the safety and health of residents.

The ruling did not provide a mechanism for a stay so that Republicans and Democrats could reach a compromise on reopening Wisconsin, which the dissenting justices wrote could endanger people in the state.

“The lack of a stay would be particularly breathtaking given the testimony yesterday before Congress by one of our nation’s top infectious disease experts, Dr. Anthony Fauci,” one of the dissenting opinions said. “He cautioned that if the country reopens too soon, it will result in ‘some suffering and death that could be avoided [and] could even set you back on the road to trying to get economic recovery.’”