Rose developed the soreness during Friday's practice. The Bulls said the decision to hold him out of the game, which was played in Rio de Janeiro, was precautionary.
"We wanted to see where he was today, but he wasn't as well as we would have liked," coach Tom Thibodeau said. "He still had the soreness. So we anticipated giving him time off. We view our training camp as the entire month. So if he needs a day, or a couple of days, we'll do that."
Kirk Hinrich started at point guard in Rose's absence and finished with eight points and three assists in the Bulls' 83-81 win.
"It's more, I think, just a precaution. He's coming off a really big injury. We're not too worried," Hinrich said. "He's been good all camp, and I'm assuming everybody is expecting him to be ready.
"Coming back from a big injury like that, you don't want to push it too hard, too fast."
Rose missed all of last season after tearing the ACL in his left knee during the playoffs in April 2012. The former NBA MVP appeared in each of Chicago's first two preseason games this month, scoring 13 points while playing at least 20 minutes in each contest.
Bulls executive vice president John Paxson said Saturday that Rose's soreness was not unexpected and that the team does not plan to have the three-time All-Star undergo an MRI.
"We never anticipated a straight line," Paxson said, according to the Chicago Tribune. "He had a little soreness and we are being ultraconservative because it's the third game of preseason.
"We know there's nothing structurally to be worried about. It's just a little soreness. If it was any other player, we'd do the same thing."
The NBA star's absence disappointed a sellout crowd of 13,635 at the HSBC Arena in Rio -- the gymnastics venue for the 2016 Olympics -- where the top ticket price for the preseason game was 2,000 Brazilian reals ($915).
Fans started chanting late in the game "Rose, Rose," hoping to see him take the floor, but Thibodeau plans on playing it safe with his star point guard.
"In training camp when guys get sore, you usually rest them," he said. "You are always concerned with injuries or soreness. We knew coming into the season he's coming off a major injury."
Thibodeau was unsure whether Rose would play in the Bulls' next game, at home Wednesday against the Pistons.
"We're not sure if he plays on Wednesday," the coach said. "Right now it's soreness, so we will just go day by day."
Chicago's Joakim Noah also missed the game, sitting out with a groin injury.
"Over the course of a season you are always going to have different issues in terms of health," Thibodeau said. "So we expect when someone is out, the next man will step up and get the job done. We had a lot of guys do that last year and we expect the same next year."
Information from The Associated Press was used in this report.