Granderson, who missed the first 38 games of the season with a fractured wrist before debuting May 14, sustained the left pinkie finger injury Friday when he was struck by a pitch from Tampa Bay's Cesar Ramos.
The three-time All-Star had appeared in just eight games, hitting .250 with a home run.
Granderson's initial injury came the first day of spring training, when he was drilled by a pitch from Toronto's J.A. Happ.
Girardi said it was uncertain when Granderson would return, indicating the outfielder was set to consult a medical specialist upon the Yankees' return to New York.
Outfielder Brennan Boesch was recalled from Class AAA Scranton/Wilkes-Barre to take Granderson's roster spot.