Granderson was hit by a pitch from Toronto's J.A. Happ in the first inning at Tampa, Florida and is expected to miss about 10 weeks, the Yankees said on their website.
X-rays revealed the extent of the injury.
The 31-year-old Granderson has spent the last three years in center field for New York but he started Sunday's game in left as the team experimented with a move that put Brett Gardner to center.
Granderson led the Yankees with 43 home runs during the regular season before his bat went cold in the playoffs and the team was eliminated by the Detroit Tigers in the American League Championship Series.
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