He is expected to be away for a week and has been replaced by Hampshire seamer Chris Tremlett.
England beat Bangladesh by 10 wickets in the first match of a triangular series on Thursday at The Oval. Jones missed the game after complaining of pain in his knee after the warm-up.
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The England and Wales cricket board said Jones's injury was not related to the career-threatening cruciate ligament injury suffered in Australia on the 2002-3 Ashes tour.