Manager Brad Mills says he first learned of Cordero's injury July 25, five days after the reliever was acquired from Toronto.
Cordero is 0-3 with a 19.80 ERA and three blown saves in six games with Houston. Mills says Wilton Lopez has assumed the closer's role.
Overall this season, the 37-year-old Cordero has a 7.55 ERA and two saves in eight chances. He is second to Mariano Rivera among active players with 329 saves.
Right-hander Mickey Storey was recalled from Triple-A Oklahoma City, where he was 7-4 with a 3.05 ERA. Storey was with the team for Friday night's game against the Braves.