The Manchester United man started Friday's 2-0 defeat to Chile at Wembley, but was withdrawn in the 57th minute and replaced by Chris Smalling.
Jones has now undergone a scan on the problem, with the Football Association confirming on Saturday that he will miss the clash with Joachim Low's side having returned to his club.
United also confirmed on their website that the 21-year-old had made his way back to Old Trafford for treatment.
It is as yet unclear whether Jones will be available for United's trip to Cardiff City next Sunday, but manager David Moyes will be hoping to have the defender back as soon as possible with fixtures against Bayer Leverkusen, Tottenham and Everton looming in the coming weeks.
Jones has made 15 appearances in all competitions for United this season, scoring one goal.
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