The 26-year-old, a key part of England's winning run this year under coach Eddie Jones, will join injured flanker James Haskell and wingers Anthony Watson and Jack Nowell among senior players on the sidelines.
"We're in agreement it's in the best interests of the player to undergo this minor procedure now," Saracens director of rugby Mark McCall told the European champions' website, adding that Kruis would be ruled out for a few weeks.
Jones has plenty of options in the second row, with Joe Launchbury or Courtney Lawes likely to partner Maro Itoje in the Autumn tests which start against South Africa on Nov. 12.
(Reporting by Ed Osmond; Editing by Toby Davis)
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