Rodriguez exited in the eighth inning Sunday after being hit in the left hand by a pitch from Kansas City reliever Blake Wood.
Rodriguez was set to start at Cleveland, batting cleanup and playing third base.
"The hand's good, the hand's really good," Rodriguez said.
Rodriguez took batting practice and fielded ground balls without any wrapping on his hand. He hit several balls into the stands and sprayed line drives around the field.
"I had him in the lineup," Yankees manager Joe Girardi said. "I went to him and said, 'You're fine, right?' He nodded, so I guess I checked with him."
Jake Westbrook was set to pitch for the Indians. Rodriguez is a career .375 hitter (9 for 24) with one home run against Westbrook.
Rodriguez hit his 599th homer on Thursday night. He is trying to become the seventh player to reach 600 home runs, and the youngest to accomplish the feat. Rodriguez turns 35 on Tuesday.
Rodriguez has six hits in 14 at-bats with four RBIs since his last home run.
"He's had good at-bats, he just hasn't hit a home run," Girardi said.
Rodriguez has hit 10 lifetime home runs in Cleveland.