The Germany star, who has stated he is unwilling to receive a coronavirus vaccine until more is known about possible long-term effects, missed Bayern's matches against Augsburg and Dynamo Kiev after being deemed a close contact of someone with the virus.
"Joshua Kimmich is self-isolating at home after testing positive for COVID-19. The FC Bayern midfielder is doing well," the Bundesliga champion said in a short statement.
ℹ️ Joshua #Kimmich is self-isolating after testing positive for COVID-19. The FC Bayern midfielder is doing well.— FC Bayern English (@FCBayernEN) November 24, 2021
The club previously announced forward Eric Maxim Choupo-Moting had also returned a positive test and could continue isolating at home.
The 32-year-old had already quarantined along with Kimmich, Serge Gnabry, Jamal Musiala and Michael Cuisance amid concerns about possible infection.
It was reported by Bild last week that any Bayern players who were forced to isolate having not been fully vaccinated against COVID-19 would have their pay withheld for the duration of their absence from first-team duties.
Head coach Julian Nagelsmann had insisted he did not fear any such measures could cause friction within the squad.
Germany boss Hansi Flick said he expected Kimmich to receive his vaccine when possible and defended the player from criticism.
"I think that it is going in this direction. We talked and I think it was a very good conversation. Now we have to wait and see," he said when asked if Kimmich would get the jab.
"Jo Kimmich is not to blame for the high number of infections. I don't think it's good that he is being pilloried in this way. It's not that easy for young people to deal with something like that."
Germany has recently seen a spike in coronavirus infections, with nearly 67,000 recorded on Wednesday, a record daily figure since the start of the pandemic.
The return of restrictions to halt the spread of the virus have been considered, while public spaces in some states have already introduced rules limiting access only to those who are fully vaccinated or have recovered from the virus.