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Davis suffered the injury during the second quarter of Sunday's 103-99 win over the New York Knicks.
After the game Davis told the media:
"I was going up for a lob, got fouled and then hit my hand on the rim...I haven't found anything out yet. Most definitely I hope it's a short-term thing. I didn't think it would keep me out, but it did."
Davis was having an outstanding sophomore season, averaging just over 18 points, 10 rebounds, and 3.6 blocked shots per game.
Davis was drafted first overall by the Pelicans in the 2012-13 NBA draft.
He tried to play through the injury but he came out of the game after getting roughed up by the Knicks Amare Stoudemire: