Putnam was released by the White Sox on Friday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Putnam underwent Tommy John surgery prior to the 2018 season before missing the 2019 campaign with a hamstring injury, but he returned to the White Sox on a minor-league deal in March. While the right-hander wasn't expected to make the major-league roster to begin the season, he'll now be a free agent.