Hutton said he was stepping aside for family reasons, The Daily Telegraph reported.
His departure comes on the heels of Works and Pensions Secretary James Purnell's resignation Thursday.
Brown reshuffled his Cabinet, promoting rival Alan Johnson to Home Secretary, replacing Jacqui Smith, who resigned Tuesday. The following day, Communities Secretary Hazel Blears announced her resignation.
Jack Straw will remain as justice secretary while Peter Mandelson's role as business secretary was expanded to include skills and science, the British publication said.
Brown also was preparing for more bad party news as full results of Thursday's local elections were expected Friday. Early returns indicate the Labor Party suffered its biggest losses in more than two decades.
Tory leader David Cameron said a general election was the only answer for the crisis swamping the government.
"We need a government that is strong, that is united, that has purpose. Instead we have a government in complete chaos," Cameron said. "I believe that all roads now should lead towards a general election."
Johnson, considered a possible replacement for Brown as prime minister, called for unity.
"I continue to believe that Gordon Brown is the best man for the job," he said.