The injury is expected to keep Ramos out through the July 31 non-waiver trade deadline.
Ramos was hurt Saturday, failing to run with full effort on a groundout to third base against the Minnesota Twins. He missed the All-Star Game because of the injury, with the Cleveland Indians' Yan Gomes replacing him on the AL roster.
Ramos is batting .297 with 14 home runs and 53 RBIs.
The Rays also reinstated lefty Jose Alvarado from family medical emergency list.