Dr. Anthony Romeo orchestrated the procedure in Chicago, repairing a tear in the pitcher's latissimus dorsi tendon and performing a debridement on his teres major tendon.
Romero executed the same operation in July 2010 on Giants right-hander Jake Peavy, who was considered to be the first Major Leaguer to fully tear the tendon, which connects the lat muscle to the humerus bone.
Peavy returned to the mound 10 months after the procedure. Rodriguez's surgery was also considered a success.
The 32-year-old A's reliever was placed on the 15-day disabled list July 4 with a strained shoulder, after pitching to a 4.20 ERA in 34 appearances. He also missed all of 2013 and much of '14 while rehabbing from Tommy John Surgery.
Rodriguez is under club control through the 2017 season.
• The A's will wait to see how rehabbing left-hander Sean Manaea responds from a simulated outing on Saturday before plotting out their rotation for next week's four-game series in Kansas City.
• The A's extended their player development contract with the Class-A Beloit Snappers of the Midwest League through 2018, they announced Friday.
Jane Lee has covered the A's for MLB.com since 2010. This story was not subject to the approval of Major League Baseball or its clubs.