Brebbia was optioned to Triple-A Memphis on Tuesday.
Brebbia will head back to the minors to clear a spot on the active roster for Tyson Ross, who was recently claimed off waivers by the Cardinals. The 28-year-old owns a respectable 3.83 ERA and 40:13 K:BB across 40 innings of relief with the big club this season, so he should be back in the majors when a fresh bullpen arm is needed.