Klose hurt his ribs in the 2-1 friendly win over Uruguay on Sunday while Reus was injured in Borussia Moenchengladbach's relegation play-off first leg against VfL Bochum and further aggravated the problem when he scored the deciding goal in the return match.
It is the third time the talented Reus, 21, who has yet to win his first cap, has been picked in the squad and dropped out through injury.
Klose's knock opens the door for Bayern Munich team-mate Mario Gomez to lead the attack after the Bundesliga top scorer made the most of a rare start by netting Germany's opening goal against Uruguay.
The 32-year-old Klose came on as a substitute in the second half but failed to make an impact.
"He picked up a painful rib injury. Medical tests on Monday showed he will need to refrain from training in the coming days and so cannot be at our disposal for the qualifiers," the German football federation said in a statement.
Germany, who top their Euro qualifying group with five wins in as many matches, meet Austria on June 3 before taking on Azerbaijan four days later.
Klose, Germany's second most capped player behind Lothar Matthaus, is chasing Gerd Muller's all-time scoring record having netted 61 times in 109 appearances.
Muller scored 68 goals in 62 internationals.
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