Clague is a surname of Manx origin. Notable people with the surname include:
Arthur Clague (1915-1983), Archdeacon of Man (the Isle of Man)
Sir Douglas Clague (1917-1981), British entrepreneur in Hong Kong
Frank Clague (1865–1952), U.S. Representative from Minnesota
Dr. John Clague (1842 - 1908) Physician and collector of Manx music
Sir John Clague (1882 - 1958), a British Civil Servant engaged in the administration of Burma during World War II
John J. Clague (born 1946), Canadian authority in Quaternary and environmental earth sciences
John Clague (1928–2004), American artist and sculptor
Paul Clegg or Clague (b. 1817) a successful fishmonger in Liverpool, the great-grandfather of the Beatle Paul McCartney