The move for Putnam was retroactive to Aug. 27.
Putnam is 3-3 with no saves and a 3.07 ERA in 41 games this season. He last pitched Aug. 26 against Boston, throwing one inning and giving up a run.
White Sox manager Robin Ventura said he had given Putnam rest hoping the groin would heal quickly, but said “it’s still there since the last time he pitched.”
Webb had been on the DL since Aug. 5 with a mild right back strain. He made three rehab appearances at Charlotte. He is 1-0 with a 2.49 ERA with the White Sox in 17 games.