Girardi said Cano hurt his hand while catching an Ivan Nova pickoff attempt at second base.
The Yankee manager didn't seem to think the injury was serious. Cano took a precautionary X-ray after the game, which came back negative. He said Cano is "day to day."
Cano told hitting coach Kevin Long that he could not swing a bat prior to his turn in the order in the eighth inning before he left the game.
Eric Chavez pinch-hit for Cano with two outs in the eighth, grounding out to end the frame in the Yankees' 5-2 win.
"He'll get some ice and some treatment and he'll be fine," said Long, who predicted that Cano will be in the lineup on Monday night in Detroit where the Yankees open a four-game series.
Cano, who went 1-for-3 with a single to right, is the Yankees' hottest hitter. He entered Sunday tied for fourth in the majors in home runs with eight. He's hit safely in 19 of his last 20 games and 22 of the Yankees' 25 games this season.
Overall, Cano is hitting .320 with 21 RBIs.
Ian Begley is a regular contributor to ESPNNewYork.com.