The Brazil defender who has been a key part of Bayern’s defence since joining the club in 2012, was forced off in the first half after suffering a deep cut to his ankle in a challenge with Zdenek Pospech.
The injury, which required 10 stitches, will rule the defender out for between 10 and 14 days.
Dante’s injury leaves Bayern further stretched in a defence already shorn of Jerome Boateng and Holger Badstuber, who miss out through suspension and injury respectively. Midfielder-turned-defender Javi Martinez, who has deputised at centre-back on occasions, is also unavailable as he has not yet fully recovered from groin surgery.
Daniel van Buyten and summer signing Jan Kirchoff look set to line up on Wednesday as they are now the clubs only fit specialist centre-backs.
On a more positive note for Bayern, Franck Ribéry could return following an ankle sprain that ruled him out of the win over Mainz.