Cuddyer got hurt during early batting practice Friday as the Twins prepared to start a three-game series in Cleveland.
Just as first baseman Justin Morneau was activated from the disabled list and it appeared the Twins were getting their full lineup back from injury, manager Ron Gardenhire lost Cuddyer, one of his best hitters.
Cuddyer is batting .295 and leads the team with 18 homers and 61 RBIs in 112 games.
Minnesota has seldom been at full strength, with former AL MVPs Morneau and Joe Mauer among several other players missing time.
Designated hitter Jim Thome, two homers short of 600 for his career, has been limited to 61 games with various aches and pains.