The uncapped Cork, 28, has played every minute of Burnley's Premier League campaign this season having joined the club from Swansea City in the close season.
“I’m really, really happy. I haven’t really got the words for it. I’m looking forward to going to meet up,” Cork told Burnley's website.
Cork has been integral part of Burnley's superb start to the season, which has seen them climb to seventh in the table, level on points with Arsenal and Liverpool above them.
Tottenham Hotspur trio Dele Alli, Harry Winks and Harry Kane had already withdrawn from manager Gareth Southgate's squad.
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West Bromwich Albion midfielder Jake Livermore and Everton defender Michael Keane were called up following the withdrawal of those three players.
Chelsea centre back Gary Cahill has reported for duty after being cleared to play by the Premier League side's medical team.
England host Germany at Wembley on Nov. 10 before the visit of Brazil four days later. All three teams have qualified for next year's World Cup in Russia.
(Reporting by Matt Westby and Toby Davis; Editing by Christian Radnedge and Ken Ferris)
