"I have been informed about his surgery and will directly speak with him," Loew said of Klose, who plays for Italian club Lazio.
Lazio said on its website Klose would start his recovery immediately after the surgery. Klose's Germany team mate Mario Gomez has already been ruled out of those games with a knee injury.
Max Kruse had been called up for the last two internationals earlier this month.
"I still do not know what kind of impact his absence will have on the nominations for the games against Ireland and Sweden. I will name the squad at the end of next week," Loew said.
Germany, top of Group C next host Ireland on Oct. 11 before finishing off away to Sweden four days later. They need two points from the two games to guarantee top spot.