The right-hander, who missed the last 2 1/2 months of 2012 because of elbow problems, was sidelined with a strained side muscle Feb. 17 and had been working on a rehab program.
That effort, however, is taking longer due to continuing soreness, Sveum said.
"It's a minor setback that (he) could wind up missing two weeks to a month," he told the Chicago Tribune. "Now you're looking at him getting two (Cactus League) starts at the most."
"It's just a body's way of saying it's just going to take a little more time," Garza told the newspaper. "It's not a setback, but just came to the realization that mind and body are (going) too fast."
Garza went 5-7 with a 3.91 ERA in 18 starts last season.