Julian Nagelsmann confirmed Kimmich missed training on Thursday as a precautionary measure and the Bundesliga champions are awaiting the results of his PCR test.
Kimmich, who has publicly confirmed he has not yet received either dose of his vaccine, was recently forced into isolation along with Serge Gnabry and Jamal Musiala due to being in close contact with Niklas Sule.
Sule withdrew from the Germany squad to face Liechtenstein and Armenia after he tested positive for COVID-19.
Kicker reported that Kimmich, Serge Gnabry and Jamal Musiala – who are all unvaccinated – are being split up for the rest of the Bayern squad due a spike in coronavirus cases.
Josip Stanisic was the latest Bayern player to return a positive COVID-19 test this week, with the Bavarian giant stating on Thursday that the fully-vaccinated Croatia defender is isolating at home but feels "fine".
Nagelsmann revealed Kingsley Coman will miss the clash with Augsburg due to a minor muscle problem, but Leon Goretzka is fully fit.
The Bayern head coach will make a late decision on whether Eric Maxim Choupo-Moting and Alphonso Davies feature on Friday after they only returned from international duty on the eve of the game.