Anderson had been in and out of the lineup over the last 10 days because of sore legs. The White Sox were hopeful he could play Tuesday against the Pittsburgh Pirates after the club had a day off Monday, but Anderson missed that game and will take more time to rest.
Anderson's placement on the IL is retroactive to Aug. 29.
"Some lingering soreness," White Sox manager Tony La Russa told reporters. "Let's get certainty that he's 100%. ... The 10 days allows that to happen."
Anderson has a .302 batting average with 14 home runs, 53 RBIs and 17 stolen bases over 108 games in the 2021 MLB season. Chicago has a 13-11 record when he isn't in the starting lineup this year.
The move comes a day after starting pitcher Lance Lynn went on the injured list with knee inflammation and Lucas Giolito departed his start with hamstring tightness.
To fill out the roster, the White Sox reinstated veteran outfielder Billy Hamilton after the completion of his rehab assignment with Triple-A Charlotte. The 30-year-old speedster returns from an oblique strain that forced him to spend August on the IL.
The White Sox also recalled right-handed reliever Matt Foster and outfielder Gavin Sheets, and the team selected the contract of infielder Romy Gonzalez. To make room for the moves, the club designated infielder Jake Lamb for assignment.