No tests on the calf are scheduled, and Rodriguez is listed as day-to-day.
Manager Joe Girardi said Rodriguez approached him after his nine-pitch at-bat in the fourth to tell him that his calf was bothering him.
"The first it came up was today," said Girardi. "He hadn't said anything before today, so I was a little bit shocked."
Ramiro Pena replaced Rodriguez initially, although after Pena was pinch-hit for in the eighth inning, catcher Francisco Cervelli moved down to the hot corner for just the second time in his big league career. Cervelli did make a catch on a popup in foul territory in the ninth.
Rodriguez has been hampered from time to time this season with hip and groin issues. He missed four games in mid-June with tightness in his right groin and a game 10 days ago with a bruise on his ankle suffered during batting practice.
Girardi wasn't exactly optimistic he would have his regular third baseman in the lineup on Tuesday.
"Would I be a little surprised if he plays tomorrow? Yes," Girardi said. "But we'll see how he is. When a guy comes out, you don't expect him to be able to play the next day. But maybe he'll be available to us as a DH. I can't really tell you."