Bundesliga leaders Bayern confirmed the news Friday, the day after Kimmich missed a training session, which head coach Julian Nagelsmann described as a "precautionary measure", on the eve of their league game at Augsburg.
Kimmich, 26, only left house quarantine Tuesday after previously having contact with Bayern team-mate Niklas Suele, who tested positive last week while on international duty with Germany.
As well as Friday's match at Augsburg, Kimmich also misses next Tuesday's Champions League away to Dynamo Kiev with Bayern already qualified for the last 16.
Kimmich, Serge Gnabry, Jamal Musiala and Eric Maxim Choupo-Moting are reportedly the only non-vaccinated players in the Munich squad.
Bayern are already without Suele and Josip Stanisic, both of whom are fully vaccinated, but have tested positive for the coronavirus.
Kimmich has been at the centre of fierce debate in Germany since revealing he opted not to be vaccinated due to "personal concerns".
He was heavily criticised and accused of neglecting his duties as a role model in Germany, which has one of the lowest vaccination rates in Europe at around 68 percent.
Germany is currently in a ferocious fourth wave of the virus with record numbers seen this week, leading health minister Jens Spahn to describe the situation as "a national emergency".
Standout matches today