Rodon, 28, is 9-5 with a 2.38 ERA in 19 starts this season and could be out longer than the required 10 days.
"We're going to err on the side of caution so it seems to me that's overly optimistic," White Sox manager Tony La Russa said. "If it happens, great, if it doesn't, we'll be patient."
Rodon reported the soreness Tuesday while the team was in Minnesota for a road series. He flew back to Chicago and is being checked by doctors to determine if it's something more serious than fatigue. The club doesn't believe so. The left-hander has a history of arm injuries and pitched only seven innings last season. He's thrown 109 innings this year.
"We're hoping it's just a short break and he'll be back sooner rather than later," La Russa said. "There's nothing unusual about our concern."
Rodon was scheduled to start the "Field of Dreams" game Thursday against the New York Yankees, but Lance Lynn will be pushed back a day to throw in that game. Right-hander Reynaldo Lopez started against the Twins on Wednesday afternoon.
"He's the best candidate," La Russa said. "He's proven to be a real asset out of that bullpen."
Lopez has a 1.59 ERA in 17 innings this year out of the bullpen after struggling as a starter in 2020. La Russa was asked if key reliever Michael Kopech was considered to take over for Rodon, who could miss multiple starts.
"He has to be considered, but we're now into August and extending him to where he would be a starter takes him out of that role that we really need him," La Russ said. "And we expect Carlos to be back."
La Russa won't see Lynn take on the Yankees as he'll miss the "Field of Dreams" game because of a death in his family. Bench coach Miguel Cairo will manager in his place.
"He's [Cairo] been talking about the Yankees for the last three days," La Russa said. "I guarantee no one will pay more attention than he will."
The White Sox called up right-hander Matt Foster to take Rodon's place on the roster while also announcing catcher Yasmani Grandal (knee) will begin a rehab assignment with Double-A Birmingham. Grandal has been out since early July after injuring his knee on a checked swing.
"Every day he's just grinding and grinding," La Russa said of his rehab.