The 27-year-old didn't start against Baltimore on Sunday, but entered the game as a pinch-hitter and went 0-for-1, snapping his 10-game hitting streak.
"He said he's good enough to play," Rays manager Joe Maddon said before Monday's game. "On this turf, it's a pretty quick field ... the ball really scoots off this stuff pretty quickly, so it's good to get him out there at third base on this field."
Rodriguez injured the pectoral muscle diving for a ball in a game May 12. He entered Monday's contest batting .228 with two homers and nine RBIs.