Castro injured himself on a diving play earlier in the day during the sixth inning of a resumed game against the Baltimore Orioles.
The four-time All-Star is hitting .283/.317/.456 with two round-trippers in 16 contests for the defending champions.
The Nationals promoted No. 2 prospect Luis Garcia to replace Castro on the major-league roster. Washington also transferred left-hander Sam Freeman to the 60-day IL and added righty Ryne Harper for the second contest against the Orioles.