The 30-year-old missed the world champions' morning training session and, after undergoing medical checks, was ruled out for their Group C qualifier.
Khedira will remain in Stuttgart for treatment ahead of Germany's second qualifier against Norway on Monday.
The Juventus player was not part of Germany's Confederations Cup-winning team in July, having been rested by coach Joachim Loew ahead of next year's World Cup in Russia.
Loew is already without winger Serge Gnabry, who left the team hotel on Tuesday with an ankle injury.
Germany, who top Group C, take on the Czechs in Prague before hosting Norway in Stuttgart three days later.
They have a maximum 18 points from six games, five ahead of second-placed Northern Ireland and nine in front of the third-placed Czechs.
(Reporting by Karolos Grohmann; Editing by Mark Heinrich)
