The 27-year-old was injured in their 0-0 draw against Botev Plovdiv on Thursday, a result that saw them advance in the Europa League on away goals from the first leg.
"The first diagnosis is a suspected torn ligament. There will be further tests to determine the exact damage," the club said in a statement. "But if the initial diagnosis is confirmed then unfortunately the defender will be out for several weeks.
Stuttgart, who boosted their squad with a string of transfers in the close season, kick off their Bundesliga campaign on Sunday with a trip to Mainz 05.