The team said in a statement that Rose is expected to resume basketball activities in two weeks.
Head coach Fred Hoiberg noted Wednesday that Rose did not have any structural damage.
"He's still in great spirits, and again, it's not a structural injury," Hoiberg said, adding that he texted with Rose on Tuesday night. "When he comes back ready to go he should be able to go right back into it 100 percent -- which, if you have something going on with one of your other body parts, it's going to be you gradually get back. You know, 50 percent load and then move all the way up from mid-restriction. I don't anticipate that in his case this will happen."
Rose's teammates, like many within the organization, can't believe the 26-year-old point guard has suffered another setback.
Rose has played in just 100 regular-season games since the 2011-12 season because of various health issues, including three serious knee injuries.
"I think he's good," center Joakim Noah said. "I mean, as good as can be. It always sucks to be injured and not be able to play the game that you love. But he'll be all right."
Cavaliers star LeBron James -- whom the Bulls face in their season opener on Oct. 27 -- echoed those sentiments.
"It's unfortunate for him," James said of Rose. "Obviously, I wasn't there at practice to see what happened, but any time someone has to have surgery it's unfortunate. I hope he has a speedy recovery."
In the meantime, the Bulls will deal with the reality that Rose will miss a couple of weeks.
"[The injury] sucks in a way," Bulls big man Pau Gasol said. "But he's a tough kid and hopefully he'll heal well and he'll be ready to go. But it's unfortunate that he won't be able to be a part of most of training camp or the preseason because it's a useful time for any team to get things on track, set the foundation for the season, especially with a new system, new philosophy, new coach. But no excuses. Life works out that way sometimes, and you just got to keep walking."
ESPN.com's Dave McMenamin contributed to this report.