The infected player, Niklas Suele, is fully vaccinated and currently asymptomatic, added the DFB.
Fellow Bayern teammates Kimmich, Serge Gnabry and Jamal Musiala as well as Karim Adeyemi of RB Salzburg, have been asked to isolate because they are close contacts of his, even though they have tested negative, DFB chief director Bierhoff said.
“This news, coming so close before the final World Cup qualifiers, is bitter for the coaching team as well as for Die Mannschaft,” said Bierhoff.
The latest high profile case comes as Germany is fighting a surge in new infections, with its seven-day Covid rate striking a new record on Tuesday.
It also puts the spotlight again on Kimmich, who had sparked a fierce debate in the country last month when he revealed he opted not to get vaccinated, because of “personal concerns”.
It even prompted Interior Minister Horst Seehofer to urge him directly to rethink his position as “vaccination is the main weapon in the fight against the pandemic”.
Kimmich appears to be in the minority as more than 90 percent of footballers and backroom staff in Germany’s top two leagues are vaccinated, according to figures released last month by the German Football League (DFL).