The length of the German player's unavailability is not yet known, the Bavarian club, currently second in the Bundesliga and leading their group in the Champions League, said in a statement.
Sane "tore a muscle fibre in the back of his left thigh" on Sunday during the 5-0 win over Freiburg, according to the club. After assisting the game's third goal, Sane had to be substituted in the 76th minute.
Scorer of four goals this season in the Champions League, the former Manchester City player was having a brilliant start to the season up to the time of his injury, having scored four more goals in the Bundesliga.
This injury comes at a bad time, a month before the World Cup in Qatar for the winger, who has been capped 47 times by Germany.
Sane joins Manuel Neuer and Lucas Hernandez on Bayern's injury table.