Anderson, 29, sat out Sunday's contest against the Texas Rangers, an 8-2 victory by the White Sox, and then will sit out Tuesday's first game of a doubleheader against the Kansas City Royals. The White Sox have the day off Monday.
Leury Garcia, primarily a second baseman, was in Sunday's starting lineup at shortstop. He was 3-for-5 with a double and two runs scored.
"We just picked a day. Seemed to make the most sense,'' manager Tony La Russa said of Anderson starting the suspension before Sunday's game.
Anderson's helmet made contact with umpire Nick Mahrley's cap during an argument about a strike call in a game against the Oakland Athletics on July 29. Mahrley had just kicked Anderson out of the game when the All-Star shortstop approached him, making contact.
The time off might come at an opportune time for Anderson, who's 0 for his past 15.
Overall, he is hitting .301 with six home runs and 25 RBIs in 79 games this season.
In other roster moves, the White Sox recalled infielder Lenyn Sosa from Triple-A Charlotte and optioned right-handed reliever Tanner Banks.
The Associated Press contributed to this report.