Hamilton, who leads the AL with nine home runs and 25 RBIs, left Sunday's win over Tampa Bay in the third inning with the injury. The Rangers beat Toronto 4-1 on Monday.
Rangers manager Ron Washington called the move precautionary, and said Hamilton is day to day. Washington said Toronto's artificial turf field did not play into his decision to sit Hamilton.
Craig Gentry took Hamilton's spot in center, batting ninth.