"Kuba with a suspected torn anterior cruciate ligament. Final diagnosis yet to be made on Sunday afternoon," the club said on Twitter during the game, which ended in a 2-2 draw.
"Jakub has to expect the worst," the Champions League runners-up added in a later statement.
"The Poland international is likely to have torn the anterior cruciate ligament. A more precise diagnosis will have to wait until Sunday."
The Poland international went down following a challenge after six minutes into the Bundesliga game.
Dortmund, last season's Champions League runners-up who take on Zenit St Petersburg in the Champions League round of 16 next month, are already without injured central defenders Mats Hummels and Neven Subotic as well as playmaker Ilkay Guendogan.
In the Augsburg match, Sven Bender scored at both ends - for Dortmund in the 5th minute and an own goal in the 56th - to put the scores 1-1, with Nuri Sahin putting Dortmund back in front on 66 minutes before Ji Dong-Won equalised again six minutes later.