Garza was injured during Sunday's game against the Cardinals, and the right-hander exited in the seventh inning of a 3-2 loss.
The Brewers lead the NL Central by one game over the Cardinals entering Tuesday's play.
The move was retroactive to Monday. The Brewers recalled right-hander Rob Wooten from Triple-A Nashville.
"It was bad enough where I had to take myself out of the game, and I don't do that," Garza said Sunday. "There's too much left in the season, and I thought I'd make the smart play."
Garza is 7-7 with a 3.58 ERA and 104 strikeouts this season.
The Associated Press contributed to this report.