Milwaukee starting pitcher Matt Garza was placed on the 15-day disabled list Tuesday with a strained muscle in his back.
The right-hander departed an exhibition game start Friday in the fourth inning with what was then described as right shoulder tightness.
Greinke, signed to a $206.5 million contract in the offseason, had his worst outing in four years, allowing seven runs, including three homers, in a 10-5 loss to the Rockies.
The playing rules committee has approved two wearable-technology devices for use during games this season, two people familiar with the decision told the Associated Press.
The Motus Baseball Sleeve measures stress on elbows