Garza hasn't pitched since he felt stiffness in his right elbow in a July 21 start at St. Louis. An MRI of his elbow showed some irritation at the tip of a bone in what is being characterized a "stress reaction."
Hoyer said Garza won't throw for at least two weeks, but he didn't rule out the possibility of his return this season.
Garza was 5-7 with a 3.91 ERA in 18 starts.
The Cubs are expected to recall left-hander Brooks Raley to make his major league debut Tuesday in San Diego.
Raley was 4-8 with a 3.62 ERA in 14 starts with Triple-A Iowa.