Bentley has vowed to stay in office despite growing calls for his resignation.
The justices issued their ruling Saturday.
Alabama Governor Robert Bentley speaks during a news conference in Mobile, Alabama July 2, 2012.
The special counsel in an impeachment probe of Alabama Gov. Robert Bentley urged a judge to let lawmakers move forward with hearings and the release of his investigative report.
Lawyers for the two-term Republican have won a temporary restraining order delaying impeachment proceedings that were set to begin Monday in the Alabama House Judiciary Committee. Bentley's legal adviser David Byrne has said the rapidly moving process hasn't given the governor time to respond.
Alabama Governor Robert Bentley walks to the podium before a news conference on Friday, April 7, 2017, outside the Alabama Capitol building in Montgomery, Ala. He says he probably saw a couple of these, and recalls language like: "I'm glad you're my friend" or "you're handsome".
The report accuses him of using state resources, including law enforcement, to hide the affair and protect his reputation, "in a process characterized by increasing obsession and paranoia". "We have no idea what the committee has planned for Monday or who its witnesses will be", Bentley lawyer Ross Garber said. The report says her suspicions of an affair were confirmed when Bentley mistakenly sent his wife a text that read "I love you Rebekah" with a red-rose emoji.
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House Judiciary Committee special counsel Jack Sharman wrote that Bentley's relationship with Rebekah Caldwell Mason was well-known within his inner circle.
"Given the significance of the issues it is certainly appropriate that the Supreme Court hear this matter quickly".
Earlier this week, the state Ethics Commission found probable cause that the Republican governor broke state ethics and campaign finance laws, accusations Bentley denies.
The development was the latest in a wild week in Alabama politics as the Republican governor battled the Republican-controlled Alabama Legislature over his possible impeachment.
"This is a great day for the Constitution of Alabama", Judiciary Committee Chairman Mike Jones said in a statement.
Lawyers for both sides must file briefs with the Supreme Court by Monday morning, but it appears impeachment can proceed. The report to the House Judiciary Committee details, among other things, the content of a text that's made headline but never revealed.