Garcia skipped a turn in the rotation before lasting just two innings in his last start on Tuesday against Houston. His stint on disabled list is retroactive to Wednesday.
The 25-year-old has posted a 4.48 ERA and 3-4 record in 11 starts this season.
St. Louis recalled right-hander Fernando Salas from Triple-A Memphis to take his roster spot. Salas led the Cardinals with 24 saves last season, but started this season 0-3 with a 6.32 ERA in 18 games.
Garcia joins a long list of Cardinals on the disabled list that includes right-handed pitchers Chris Carpenter, Scott Linebrink and Kyle McClellan, outfielder Skip Schumaker and first baseman Lance Berkman.