Rodriguez (elbow) was moved to the 60-day disabled list in order to make room for Bartolo Colon on Monday.
Rodriguez has been dealing with elbow inflammation since mid-March and opened the season on the 10-day disabled list. There hadn't been any indication that the issue was particularly serious, but now he'll be ineligible to return until late May. The 25-year-old will push for a bullpen spot once he returns from his injury.