Klose, 35, who earlier this month equalled Gerd Mueller's record of 68 international goals for Germany, underwent surgery on his right foot on Wednesday in Munich and is expected to be out for at least the next two weeks.
With Germany five points clear at the top of their qualifying group and needing just a point to make it to next year's finals, the Lazio striker will miss the games at home to the Republic of Ireland in Cologne on 11 October and four days later in Stockholm against Sweden.
"The operation went well, but I had to have it done as I have been playing for a few weeks in pain," Klose told daily newspaper Bild. "I will do all I can to be back as soon as possible to play for Lazio and Germany."
Germany are also without Fiorentina's Mario Gomez, who has a knee injury, leaving third-choice striker Max Kruse of Borussia Moenchengladbach as an option. Bayer Leverkusen striker Stefan Kiessling could be recalled having repeatedly been overlooked by Loew since the last World Cup.