Rodriguez (shoulder) was outrighted to Triple-A Nashville on Thursday.
The Athletics made a slew of roster moves to clear space on the 40-man roster, and given the fact that Rodriguez isn't expected to pick up a baseball for another few months, they decided to leave him off the 40-man roster. The 32-year-old struggled in the big leagues this season, posting a 4.20 ERA out of the Oakland bullpen, so he'll likely act as organizational pitching depth going forward.