Miley also missed the start of the season with left elbow inflammation. He is 1-0 with a 3.38 ERA in three starts in his first season with Chicago.
The 35-year-old Miley hasn't pitched since he worked six innings of three-run ball in a 5-4 victory over Arizona on May 22. The IL move was made retroactive to Thursday.
"I don't think it's that big of a deal," manager David Ross said. "I think he'll be back soon. I'm not too worried."
Right-hander Mark Leiter Jr. was recalled from Triple-A Iowa. Leiter is 0-1 with a 6.57 ERA in five appearances with the Cubs this year, including three starts.
The Cubs also placed reliever Chris Martin on the bereavement list before their series finale against the crosstown White Sox. There was no corresponding move announced on Sunday.
The absences of Miley and Martin put the Cubs in a particular bind with their upcoming schedule. They play doubleheaders on Monday against Milwaukee and Saturday against St. Louis. They don't have another day off until June 6.
"Yeah, we've got a lot of innings to cover," Ross said. "We've got some guys banged up. Try to do the best we can to cover those and map them out as good as we possibly can and see where guys are at."