Right-handed reliever Sam Tuivailala was optioned to Triple-A Memphis.
Garcia was 3-3 with a 1.69 ERA in seven starts, the last coming on June 24 at Miami.
The 29-year-old Garcia combined with two relievers for a no-hitter in a rehab start at Class A Peoria last Thursday, working the first five innings.
Tuivailala is 0-1 with a 1.80 ERA and didn't allow a run in his last eight appearances covering eight innings, with seven strikeouts in that span.
