Gundogan, who joined Dortmund from Nuremberg in 2011, was limited to just three appearances last season because of the problem that forced the Germany international to miss the FIFA World Cup.
Dortmund have now revealed that Gundogan underwent a "minimally invasive" surgical procedure and expect him to be on the sidelines for another three months.
A statement on the Dortmund official website read: "The doctors believe that rehabilitation will take three months to complete.
"There should be nothing to prevent Gundogan from returning to action."
Gundogan has enjoyed great success during his time at Signal Iduna Park and was part of the side that won the Bundesliga and DFB-Pokal double in 2011-12.