"Whenever we get on this turf six days in a row, it was a concern last year for some of our guys," Girardi said. "That's partly because of age, and we try to manage them carefully. Sometimes you can run them into the ground, and then they're not productive when they're playing, so you have to pick your days."
Rodriguez did come off the bench in the 10th inning of the Yankees' 3-2 win, delivering a single for the first pinch-hit of his career (1-for-15).
Girardi said that his hope is that the 38-year-old Rodriguez will be able to play in all three of the night games at Toronto.
Rodriguez's production has cooled since an emotional nationally televised game a week ago against the Red Sox in Boston. In five games since his plunking and homer off Ryan Dempster, Rodriguez has gone 2-for-18 (.111) with seven strikeouts.
"Sometimes you just make decisions because you think it's the right thing to do," Girardi said. "Guys are going to want to be out there, but I think sometimes putting him out there becomes counterproductive over a long period of time."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.