By temporarily freezing the rule the high court's order signals that opponents have made a strong argument against the plan. A federal appeals court last month refused to put it on hold.
The court's four liberal justices said they would have denied the request.
The plan aims to stave off the worst predicted impacts of climate change by reducing carbon dioxide emissions at existing power plants by about one-third by 2030.
Appellate arguments are set to begin June 2.
The compliance period starts in 2022, but states must submit their plans to the Environmental Protection Administration by September or seek an extension.
Many states opposing the plan depend on economic activity tied to such fossil fuels as coal, oil and gas. They argued that power plants will have to spend billions of dollars to begin complying with a rule that may end up being overturned.
Implementation of the rules is considered essential to the United States meeting emissions-reduction targets in a global climate agreement signed in Paris last month. The Obama administration and environmental groups also say the plan will spur new clean-energy jobs.
To convince the high court to temporarily halt the plan, opponents had to convince the justices that there was a "fair prospect" the court would strike down the rule. The court also had to consider whether denying a stay would cause irreparable harm to the states and utility companies affected.