The team said Sunday he suffered a non-displaced fracture at the base of his right middle finger in the fourth and final inning of Saturday's rained-out game against Philadelphia when he was hit by a pitch.
He was placed on the 15-day disabled list, retroactive to March 23.
"I was hoping (Granderson) was OK," Dave Dombrowski, the team's president/general manager, said on the team's Web site Sunday. "But I also saw that he was shaking his hand."
The speedster made major league history in 2007 when he was the second player ever to compile at least 30 doubles, 20 triples, 20 home runs and 20 stolen bases in a single season.
In all, he batted .302 with 23 home runs, 74 RBI, 38 doubles, 23 triples and 26 stolen bases.