However, Butler will not need surgery to repair the injury, a league source confirmed to ESPNChicago.com.
Butler was diagnosed with a Grade 2/3 ulnar ligament sprain and a small bone impaction injury after undergoing an MRI on Monday, one day after he was injured in a loss to the Los Angeles Clippers.
He suffered the injury when he collided with Clippers center DeAndre Jordan three minutes into the second half Sunday and did not return.
The hope within Butler's camp is that rest and treatment will allow him to come back before the regular season ends and get a few games under his belt alongside Derrick Rose, who is expected to be out four to six weeks after having knee surgery Friday.
Butler, who became an All-Star for the first time this season, has been the Bulls' best two-way player this season, averaging 20.2 points, 5.9 rebounds and 3.3 assists in 55 games.
The Bulls are trying as best as they can to keep a positive attitude in the wake of the latest injury news, but veteran Kirk Hinrich knows the Bulls are in a tough spot.
"[Butler] is a two-way player, All-Star, he's just having an unbelievable year," Hinrich said. "It's a huge loss but, you know, we've kind of been through this before."
Gibson has been dealing with the same injury throughout the season and was not putting any weight on the ankle after Friday's game.
"I guess when it rains, it pours," Hinrich said. "We can't sit around feeling sorry for ourselves. Nobody else is going to. We've got to find a way."
Bulls head coach Tom Thibodeau echoed those sentiments.
"It's the nature of the league," Thibodeau said of all the injuries. "No one's going to feel sorry for us. We just got to get out there and we got to get it done."
Thibodeau, who likes to use the phrase "next man up," in reference to a no excuse policy in regards to injuries, was was asked who the next man up would be for the Bulls at this point. The veteran coach was quick with a response.
"Our team," Thibodeau said. "Whoever's next, get out there, get it done ... it's our reality. We got more than enough to get it done."