A former judge-executive of Kentucky’s Jefferson County, McConnell has helped steer the federal judiciary sharply to the right, having the Senate speedily confirm Republican nominees.
Several of Mr McConnell’s colleagues wished him well on Thursday.
“Susan and I are keeping @LeaderMcConnell in our prayers and wish him a speedy recovery," Republican Senator Thom Tillis posted on Twitter, referring to his wife.
Democratic leader Chuck Schumer, speaking on the Senate floor, also offered well wishes, saying: “I join every single one of my colleagues in wishing Leader McConnell a speedy and full recovery now.”