The court issued a brief order Monday blocking any new same-sex unions in the state.
The order follows an emergency appeal by the state following the Dec. 20 ruling by U.S. District Judge Robert Shelby that the state's ban on same-sex marriage violates gay and lesbian couples' constitutional rights.
More than 900 gay and lesbian couples have married since then.
The high court order will remain in effect until the Denver-based 10th U.S. Circuit Court of Appeals decides whether to uphold Shelby's ruling.