Team physician Brian Cole, who also repaired Rose's torn left ACL, will perform the surgery.
Bulls coach Tom Thibodeau said a timetable for Rose's return will not be determined until after the surgery, but two sources told the Tribune that he could be out up to six months if he chooses to have the meniscus reattached.
If Rose is able to have a mere arthroscopic process to clean up the meniscus, he could return this season. However, it is not known if the meniscus can be salvaged. Having a full reattachment is considered better for his long-term future.
"We're hoping for the best," Thibodeau said. "We of course feel very badly for Derrick. I talked to him at length (Saturday) night. He's in good spirits, about as well as can be expected under the circumstances. And he's already thinking about his rehab. Typical Derrick, he's concerned about his team, his teammates.
"That being said, we can't feel sorry for ourselves. We're the Chicago Bulls. We have one goal and that's to win. I believe we have the personnel in that locker room to get it done."
Kirk Hinrich will replace Rose at point guard and Marquis Teague will back him up.
"There's of course the disappointment for Derrick because of the type of person he is," Thibodeau said. "He's such a great teammate along with being a great player. But I think we have an understanding of what we need to do. We can't feel sorry for ourselves. We have to circle the wagons and get out there and get the job done."
If Rose, 25, misses the rest of the season, he would have played in just 50 games in his last three seasons.
Rose sat out the 2012-13 season with a torn left ACL suffered in April 2012.
"I think his mental toughness is going to serve him well," Thibodeau said. "I think whenever he has faced any adversity, I think his mental toughness has gotten him through. I could tell talking to him (Saturday) night there was a resolve and determination. We expect him to make a full recovery. It's another bump in the road. He'll get past it."