The move was made Monday before the A's played at Minnesota. Left-handed reliever Daniel Coulombe was also optioned to Triple-A Nashville, and the A's brought up bullpen reinforcements from the Triple-A club in righty Andrew Triggs and lefty Patrick Schuster.
Rodriguez was removed Sunday against Pittsburgh after facing one batter in the eighth inning. He'll undergo an MRI test for further examination. Rodriguez, who has a 4.20 ERA in 40 2/3 innings, is one of 11 players and six pitchers on the DL.
To put Schuster on the 40-man roster, the A's recalled outfielder Andrew Lambo from Nashville and placed him on the 60-day DL. Lambo is recovering from testicular cancer surgery.