Gnabry, who has already missed games due to a hip injury and a fractured arm earlier this season, came on in the 66th minute of Saturday's match but limped off the pitch just five minutes later.
"Serge Gnabry suffered a muscle tendon injury in the left adductor area during the 5-1 defeat in Frankfurt on Saturday," Bayern said in a statement.
"Gnabry, who had to come off after just five minutes in Frankfurt after coming on as a second-half substitute, will therefore miss the upcoming games."
Bayern, second in the league standings, next travel to face Manchester United in a Champions League clash on Tuesday, before hosting VfB Stuttgart on Sunday.