The 6-foot-3 inch long-range shooter suffered the injury in the third quarter of Friday night's 100-83 win over the Phoenix Suns. An MRI Saturday revealed the extent of the damage.
"This really hurts our team," said Chicago General Manager John Paxson. "There is really nothing we can do to make up for it."
Hinrich was examined by Dr. John Fernandez and Bulls team physician Dr. Brian Cole. He is scheduled for surgery Tuesday at Chicago's at Rush University Medical Center.
So far this season, the 27-year-old Hinrich has played in six games, with averages of 8.3 points, four assists and 1.8 rebounds per contest.
In his NBA career, the former Kansas University product is averaging 14.3 points, 6.3 assists and 3.5 rebounds in 395 regular season games.
Before the injury, he had missed just 21 games in six NBA seasons.