Hamilton hurt his right shoulder on a head-first slide into home plate during Tuesday's 5-4 loss to the Tigers at Comerica Park in Detroit.
Daniels said the reigning American League MVP has a small fracture in the humerus bone, and will not be able to swing a bat for about four weeks.
Hamilton is batting .333 with seven RBI over 11 games so far this the season for the 8-2 Rangers.
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