Reus left the team hotel on Wednesday evening after team doctors diagnosed the injury.
"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.
"Further treatment will be undertaken at Borussia Dortmund."
The 26-year-old has had a long list of injuries in his career, one of which ruled him out of the World Cup last year on the eve of the team's departure for Brazil.
Germany take on Group D leaders Poland in Frankfurt on Friday before travelling to Glasgow to face Scotland three days later. They are second in the group on 13 points from six matches, one behind the Poles and two ahead of third-placed Scotland.