Rodriguez (shoulder) was transferred to the 60-day injured list by the Diamondbacks on Wednesday.
Rodriguez experienced further tightness in his left shoulder after throwing a bullpen session Friday, Nick Piecoro of The Arizona Republic reports.
Manager Torey Lovullo said Rodriguez (shoulder) could throw off a mound within the next week, Theo Mackie of The Arizona Republic reports.
Arizona placed Rodriguez (shoulder) on the 15-day injured list Thursday.
Rodriguez threw from 60 feet Tuesday, Jody Jackson of Bally Sports Arizona reports.
Rodriguez will begin the season on the injured list after being diagnosed with a strained left lat, Nick Piecoro of The Arizona Republic reports.
Diamondbacks manager Torey Lovullo said the medical staff was "encouraged" after examining Rodriguez (lat) on Wednesday, Theo Mackie of The Arizona Republic reports.
Rodriguez allowed two runs (one earned) on four hits while striking out four over four innings in Saturday's spring start against the Reds.
Rodriguez allowed three runs on five hits and two walks while striking out four over three innings in Sunday's spring start against Milwaukee.
Rodriguez allowed four runs on four hits and two walks while striking out two over one-plus innings in Tuesday's spring start against Texas.