The versatile Germany international was withdrawn in the 60th minute of the clash at Signal Iduna Park, which saw the visitors hold on to claim all three points through Raul Bobadilla's goal despite Christoph Janker's red card.
And that loss has proven doubly costly with Grosskreutz, who can operate on the wing as well as in central midfield and at full-back, reduced to the role of spectator until March.
"Borussia Dortmund will be without Kevin Grosskreutz for the next six weeks," a statement on Dortmund's official website read.
"The all-rounder, who was used as a full-back in the game against Augsburg, went off on Wednesday night with a small tear to the thigh muscle.
"The medical department expects that Grosskreutz will be out for about six weeks, so he could perhaps be ready for the Champions League second leg against Juventus on March 18."
However there is better news for the Bundesliga's bottom club surrounding full-back Lukasz Piszczek.
Piszczek was kept out of the game against Augsburg after struggling with a problem in training but, ahead of Saturday's trip to Freiburg, coach Jurgen Klopp said: "He [Piszczek] seems much better to go."
