The injury happened during Sunday's game 4 between the Kings and the Golden State Warriors.
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Reports say there is still hope Fox will play Game 5 but would need to play with a protective covering on the finger, according to a tweet by ESPN's Adrian Wojnarowski.
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Fox has followed up a breakout season with a stellar postseason, averaging 31.5 points, 6.0 rebounds and 7.0 assists in his playoff debut, ESPN reports. He scored 38 points in nearly 40 minutes in Sunday's Game 4 loss to the Warriors.
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The Warriors and the Kings are tied in the series at 2-2.
Game 5 will be at Golden 1 Center in Sacramento at 7 p.m.
ESPN contributed to this report