Kimbrel was placed on the IL due to right elbow inflammation, according to the team. He will be out at least another week as the roster move was retroactive to Monday.
"I still think the story has yet to be written about his contribution this year," Cubs president of baseball operations Theo Epstein told reporters. "If this goes according to plan and he feels good and we get him back, he could save a lot of big games for us the rest of this month and, hopefully, next month."
Kimbrel has a 5.68 ERA and 26 strikeouts across 19 innings (21 games) this season. He recorded 42 saves with the Boston Red Sox last season and became a free agent this year, reaching a three-year deal with the Cubs on June 7.