Precautionary X-rays taken after the game were negative, and Cano said through a Yankees official that he hopes to play on Monday night in Detroit.
Cano injured the hand while catching a pickoff throw from starter Ivan Nova.
"He talked about it after his third at-bat," Girardi said. "It was kind of difficult, that at-bat. I asked him if he could play defense for a couple of innings; he said, 'No problem.'"
Eric Chavez appeared in the eighth inning as a pinch-hitter for Cano, who had been 1-for-3 and played in all but eight games since the 2007 season began. In '06, Cano's first full big league season, a left hamstring injury limited him to 122 games.
Eduardo Nunez played second base for the Yankees in the ninth inning.
Right fielder Nick Swisher is now the only Yankee to have played every inning of every game in 2011.