It said Loew needed to be taken to hospital due to "the effects of a sports accident" that had squeezed an artery and required treatment.
Loew will be replaced on the bench by his assistant Marcus Sorg for their June 8 qualifier against Belarus in Borisov and their home match against Estonia three days later.
"I feel well again but I have to take it easy for the next four weeks," Loew said in the DFB statement. "I am in constant touch with the coaching staff and will remain in tight contact over the phone ahead of the two matches."
Germany want to play a strong qualifying round as they look to rebuild after last year's World Cup first round exit that shocked the soccer-mad nation and the surprise Nations League relegation.
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The Germans are third in the Euro 2020 qualifying Group C on three points, three behind leaders Northern Ireland, but with a game in hand.
(Reporting by Karolos Grohmann; Editing by Amlan Chakraborty)
