The reigning National League batting champion said Monday before a game with San Francisco that the injury is "extremely frustrating" and more "nagging than anything else." He said he can run only at about 70%. The move is retroactive to April 18.
Cuddyer is batting .317 with three home runs and 10 runs batted in this season. A season ago, Cuddyer led the league with a .331 average.
Colorado recalled infielder Charlie Culberson from triple-A Colorado Springs to fill Cuddyer's spot on the roster.
Reliever Jared Hughes was recalled from triple-A Indianapolis before Monday night's game against the Cincinnati Reds.
Rodriguez was 0-2 with a 7.65 earned-run average in four starts. He did not pitch after June 5 last season because of tightness in his forearm but has said since the start of spring training that his arm feels fine.
Giambi missed Cleveland's first 18 games because of a rib fracture suffered during spring training.
To make room for Giambi, the club optioned reliever Blake Wood to triple-A Columbus. He was 0-1 with a 7.11 ERA in seven games.