Hamilton leads the majors with a .359 batting average and has 31 home runs and 95 RBIs. He was in the starting lineup as the designated hitter Tuesday night at Kansas City.
Hamilton was set to get the shot after the game and then sit out Wednesday for the AL West leaders.
Rangers assistant general manager Thad Levine said Hamilton had a similar shot, called Synvisc, in April for discomfort in the same knee.
Hamilton was originally listed as the center fielder Monday, but was moved to DH.