The Brewers went into Tuesday night's game against the Cubs in Chicago trailing NL Central-leading St. Louis by one game, which grew to two when the Brewers fell to the Cubs 6-4 and the Cardinals topped the Pirates 6-4.
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.
The Associated Press contributed to this report.