Klose, joint Germany all-time top scorer with 68 goals, was injured in Lazio's 1-1 draw against Parma in the Serie A and taken off six minutes from time.
"He is now in Munich, being treated by federation doctors," the German football association said in a statement.
The 35-year-old had only returned to action in October after undergoing foot surgery that had ruled him out for a month.
Germany, who have qualified for next year's World Cup in Brazil, will play Italy in Milan on Nov. 15 before taking on England in London four days later.
- Sports & Recreation