It is unclear exactly when Rose's injuries occurred. He was 2-for-6 in the first half, with four points and one assist.
Bulls coach Fred Hoiberg said Rose's hamstring was the issue, and he will be reevaluated Tuesday.
"It's tough," Hoiberg said. "We knew Derrick had a little bit of soreness before the game, and unfortunately, he went down. We were shorthanded going into this one at the point guard spot, so that didn't help. But you got to find a way to fight through those times. We didn't do that. We did not do a good job. I thought we let a lot of little things bother us tonight, and it affected us out there on the floor."
Rose has missed six games because of injuries so far this season. He missed almost all of training camp because of a left orbital fracture, and he missed a handful of contests because of knee tendinitis and knee and hamstring soreness.
Rose's absence left the Bulls even more shorthanded Monday.
Hoiberg is hopeful that all his point guards will be back on the floor soon. The Bulls' next game is Thursday against the Lakers, the first game of a seven-game road trip.
"With Kirk, it's the thigh," Hoiberg said. "He took a big hit and had a bruise there. E'Twaun has a little tweak in his hamstring. Derrick, he was great this morning. Something happened from the shootaround to game time, where he got a little bit of soreness, and unfortunately, when he went out there tonight, it got worse. We had to sit him. It is tough, but at the same time, next man up. We have to come in and perform."
The Bulls are currently carrying the maximum of 15 players on their roster. Hoiberg said it is too early to know if another move will be in order to sign a different point guard.
"We'll hopefully get them back soon," Hoiberg said. "It's too early to say. We'll reevaluate it and see how it looks."
Information from The Associated Press was used in this report.