Rodriguez, 35, allowed four runs in four innings on Saturday. He has a 7.65 ERA and a 1.60 WHIP in 20 innings this year, including a league-high seven home runs allowed. Wandy missed most of last season with elbow and forearm problems.
Right-hander Jared Hughes has been called up from Triple-A to replace Rodriguez in the roster. The 28-year-old has a 3.49 ERA in 118 2/3 relief innings for Pittsburgh over the last three seasons.
It's unclear who will replace Wandy in the rotation, but long relievers Jeanmar Gomez and Stolmy Pimentel are candidates.