Hamilton, who has missed 12 games this season with injuries, said he aggravated his groin and thigh bruise during Sunday's loss to the Miami Heat.
After playing Sunday, he sat out Monday's victory over the Washington Wizards.
Hamilton is expected to get an extended rest period to recover from injuries he said makes him feel as if he is "playing on one leg."
"Rip is a terrific player. And he plays both ends, so I'm concerned about him with this thing becoming recurring," Bulls coach Tom Thibodeau said Wednesday. "So I want to make sure this time he's completely healthy. I think a guy like that, you've just got to be careful with. So that's what we're going to do."
Hamilton, who has missed more games (12) than he has played (11), said his body isn't allowing him to stay on the floor.
"Last game, it was killing me the whole second half," Hamilton said. "And then the next day it was even 20 times worse. It's one of them things, you want to be out there. I know everybody says look at the big picture, look at the end, but it's tough because you want to be out there now. You want to play now. And my body's not allowing me to play right now."
Deng will miss his sixth straight game after tearing a ligament in his left wrist. It is possible he returns Thursday when the Bulls take on the New York Knicks, according to Thibodeau.
"It's hard to measure each day," Thibodeau said. "He's doing a lot of individual stuff without contact. [Tuesday] he had some contact with [Brian] Scalabrine so that was a good sign. ... We want to make sure he can handle everything. We just want to be patient. He's doing fine. He's moving in the right direction."
Nick Friedell covers the Bulls for ESPNChicago.com and ESPN 1000.