Lilly has a strain on the right side of his rib cage.
Matt Magill will take Lilly's place on the mound against the San Francisco Giants. He made his major league debut last week in a no-decision against Milwaukee.
Lilly gave up five runs on eight hits in three innings during a 12-2 loss to Colorado last Monday. The 37-year-old hurler has an 0-1 record with a 5.63 ERA in two starts.