The right-hander has posted a 3.74 ERA and a 7-7 record over 22 starts this season.
Garza missed the first seven weeks of the 2013 season with the Cubs after suffering a similar oblique injury during spring training.
The Brewers called up Rob Wooten from Triple A Nashville to replace Garza on the roster. Wooten has a 4.36 ERA in 37 appearances for the Brewers this season.
The Brewers opened Tuesday at 61-51, in first place in the National League Central.
- Chris Johnson