Stroman, 32, had been scheduled to come off the injured list to pitch on Wednesday against the White Sox, but he experienced discomfort in his ribs following a bullpen session in Toronto on Sunday. Stroman, who was already nursing a sore hip when the fracture occurred, underwent an MRI on Monday.
"It's an unusual injury for a pitcher," said Jed Hoyer, the Cubs' president of baseball operations. "We found out on Sunday he was having some issues. We didn't know if it was muscular, we didn't know if it was skeletal. We didn't know if it was indigestion. We didn't know what it was."
Stroman hasn't pitched since going on the injured list after his start on July 31. He gave up six runs in three innings in that outing, capping a rough month after a solid start to his season. He posted a 9.11 ERA in July after compiling a 2.59 mark over the first three months of the season.
Hoyer was asked if Stroman could miss the rest of the season.
"I have no idea," he said. "That's the honest truth. We don't know at this point. We'll give him a real rest period and see how he feels."
Added manager David Ross: "We have to wait and see. I know he'll try to work his way back and help us out."
In Stroman's place, righty Javier Assad will get the bulk of the starts, including Wednesday night's six-inning effort against the White Sox, in which he allowed three runs (two earned) on four hits and two walks and struck out four in a 4-3 victory. It was Assad's 12th start in his two-year big league career.
Assad has a 3.11 ERA in 22 games this season, with most of the appearances coming in relief.
"Assad has been fantastic for us in all these different roles," Hoyer said. "Hopefully someone else will step up during this period."
Chicago is already navigating around another struggling pitcher, Drew Smyly, though he's likely to return to the rotation after being sent to the bullpen recently. Smyly picked up the win Wednesday night after pitching a scoreless ninth.
The Cubs are in the wild-card and division races in the NL after a win streak just before the trade deadline allowed the team to add instead of subtract from its roster. But the starting staff has been up-and-down lately, contributing to a 4.84 team ERA since the All-Star break. That's good for just 10th in the NL entering play Wednesday. Now the Cubs will be without a veteran starter for the near future.
"We'll move forward with the guys we have now," Hoyer said. "Hopefully we'll keep playing well."