The 26-year-old Borussia Dortmund player left the team hotel on Wednesday after doctors confirmed that he would not be able to take part in the upcoming matches.
“The painful injury which the 25-times capped international sustained in the Bundesliga match against Hertha Berlin (last week) makes his participation in the two international matches impossible,” the German team said in a statement on Thursday.
“Further treatment will be undertaken at Borussia Dortmund.”
The midfielder’s career has been plagued with injuries, one of which sidelined him from the World Cup last year. Germany face Group D leaders Poland here on Friday and then travel to Glasgow to face Scotland three days later.
The reigning World Champions are currently second in the group on 13 points from six matches, a rung below Poland.