The incident occurred in the dressing room after Bayern Munich were beaten 3-0 by Manchester City in the first leg of their Champions League quarterfinal tie on Tuesday.
The pair were seen arguing towards the end of the encounter at the Etihad Stadium and matters got out of hand off the field as well.
Mane and Sane had to be separated by teammates, with the latter coming out worse with a bleeding lip.
On their arrival back in Germany, Mane took the team bus while Sane was seen going home in a private vehicle.
Bayern have now confirmed that Mane will not be part of the squad for Saturday's Bundesliga encounter against Hoffenheim while the Senegalese will also be hit with a fine.
A statement from Bayern read: "Sadio Mane, 31, will not be in the FC Bayern squad for the home game against 1899 Hoffenheim next Saturday. The reason is Mane's misconduct after FC Bayern's Champions League game at Manchester City. In addition, Mane will receive a fine."
Mane has scored 11 goals and provided five assists in 32 appearances for Bayern Munich since joining from Liverpool last summer.
