The Giants placed Rodriguez on the 10-day injured list Saturday due to right elbow neuritis, John Shea of the San Francisco Chronicle reports.
The injury may have cropped up during Friday's game against the Padres, when he entered the game in the ninth inning as a pinch hitter for Bryce Eldridge. Rodriguez will be sidelined until at least mid-August, and in a corresponding move, the Giants recalled Nate Furman from Triple-A Sacramento.