The speedy outfielder continued to undergo pregame treatment, and Girardi said that if he came through it OK, he could be available to play at some point in the Yankees' series finale.
But the preference is to avoid using him.
"If you could, you would like to," Girardi said. "I've got to see if he's available after a couple hours."
New York is off on Monday, potentially giving Gardner two full days of rest.
Gardner entered Sunday hitting .272, with eight RBIs and six stolen bases through 23 games.
Ichiro Suzuki started in left field and batted ninth for the Yankees on Sunday.
Chris Iseman is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.