The winger will miss Thursday's (AEDT) UEFA Champions League clash with Atletico Madrid and a string of domestic matches, though Bayern confirmed he was "doing well" and was "otherwise in good health."
Former Arsenal youngster Gnabry was a key figure in the Bayern side which won the Bundesliga, DFB-Pokal and Champions League treble last season.
Bayern boss Hansi Flick has strong reserves in midfield and attack, but Gnabry's loss deals him a blow, given the Germany international is an established first-team regular.
ℹ️ Serge Gnabry has tested positive for Covid-19. He is doing well and is currently in quarantine. pic.twitter.com/ZMYliMAiy6— FC Bayern English (@FCBayernEN) October 20, 2020
The club issued a statement that read: "Serge Gnabry, 25, has tested positive for COVID-19. The FC Bayern attacker is otherwise in good health and is self-isolating at home."
In the Bundesliga alone, Gnabry scored 12 goals and had 10 assists in 2019-2020, and he began this season with a hat-trick against Schalke.
Gnabry was also highly influential in Europe last term, netting nine goals in 10 games.