The Grizzlies did not provide a timetable for his return, saying only that they would provide an update in approximately two weeks.
"It's unfortunate," Grizzlies coach David Fizdale told reporters Friday. "But watching him play in pain like that and really trying to push through that stuff was worse to watch."
Conley will undergo therapy to help in the healing process after consulting with physicians and the team's medical staff.
"Obviously, we're feeling more for him. It's been a frustrating process," Fizdale said. "He did so much work this summer to get ready for this year to play the style of play after a year under his belt of knowing how I wanted to play, and for whatever reason this thing isn't going away on its own."
The guard has started 12 of the Grizzlies' first 14 games this season. Conley is averaging 17.1 points, 2.3 rebounds, 4.1 assists in his 11th NBA season. He has been playing an average of 31.1 minutes each game.
Conley sat out Wednesday night's 116-113 loss to Indiana and also missed a Nov. 1 game against Orlando.
Mario Chalmers will contine to start in Conley's absence, but Fizdale made the caveat that "I'm looking at everything to help these guys."
The Grizzlies (7-7) are fourth in the Southwest Division, and next host the first-place Rockets (12-4) on Saturday night.
"We'll figure it out," Fizdale said. "These guys have connected, they're going to come together, and we'll make it work until [Conley] comes back to us."
The Associated Press contributed to this report.