Hamilton, 29, sustained a small fracture of the humerus below his right shoulder during the first inning of the Rangers' 5-4 loss yesterday to the Detroit Tigers.
"Our medical staff said six to eight weeks is the general rule of thumb on this injury," Rangers General Manager Jon Daniels told MLB.com. "When he does come back, we expect him to be 100 percent and not have any complications."
Third-base coach Dave Anderson sent Hamilton home on a foul popup near the Tigers' bench when he saw no one was covering the plate. Hamilton tried to slide head first and reached out his right arm to touch the plate when catcher Victor Martinez went for the tag.