The 25-year-old Germany centre back is the second Bayern player to be pulled out of action after Serge Gnabry's false positive test in October. Gnabry has since returned.
Bayern, who won five titles in 2020 including the Champions League and the domestic league and Cup double, travel to title rivals Borussia Dortmund on Saturday.
Meanwhile, Real Madrid defender Eder Militao has tested positive for COVID-19 ahead of their Champions League home game against Inter Milan, the Spanish champions said on Monday.
"Our player Eder Militao has given a positive result in the COVID-19 tests carried out on Sunday morning," Real said on its website.
The club added that all other first-team players and coaching staff, as well as the club employees who work directly with them, had tested negative both on Sunday and Monday.
Eder Militao will miss Real Madrid's match against Inter Milan after testing positive
Real, who are bottom of Champions League Group B, face third-placed Inter on Tuesday.
Six Dynamo Kiev players and five members of staff have tested positive before Wednesday's Champions League group game against Barcelona, the Ukrainian club have said.
"Testing showed a positive result in several players of the team: Georgy Tsitaishvili, Denis Garmash, Mikkel Duelund, Alexander Karavaev, Tudor Belutse and Mykola Shaparenko," Dynamo said in a statement.
"In addition, the tests of assistant head coach Emil Karas and four representatives of the team's staff gave a positive result."
Dynamo are third in Group G with one point, five behind leaders Barcelona, who they play in Spain on Wednesday.