Greinke (4-1) allowed four runs on eight hits while striking out four over six innings in Tuesday's 4-2 loss to the Brewers.
The Astros mustered little in the way of an attack against Milwaukee pitching, and Greinke was handed his first loss since being traded to the Astros. The club has now lost two straight games started by Greinke after winning the first four. The right-hander will look to get back on the winning track Monday at home against Oakland.