The Brewers went into Tuesday night's game against the Cubs in Chicago trailing NL Central-leading St. Louis by one game.
Gomez injured his wrist swinging a bat in Milwaukee's 15-5 loss to San Francisco on Sunday.
The two-time All Star will remain available as a pinch-runner and defensive replacement, but he will not swing a bat until Sunday.
The Brewers say Gomez isn't going on the disabled list. Manager Ron Roenicke admits the injury could potentially keep Gomez out of the lineup for a couple of weeks.
"It's going to take some time," Roenicke said.
Gomez is batting .281 with 21 home runs and 29 stolen bases this season.