Giants manager Bob Melvin said Sunday that Rodriguez (elbow) will be shut down from throwing for at least a couple weeks, Shayna Rubin of the San Francisco Chronicle reports.

The right-hander landed on the injured list Thursday due to elbow inflammation, and that diagnosis was confirmed after undergoing an MRI. Rodriguez has yet to be ruled out for the season, but he'll likely need to avoid any setbacks in his recovery to have a chance of rejoining the Giants in late September.