Smith, the National Football League's leading scorer and the key to the Super Bowl champions' running game, went down in the third quarter of a 24-16 victory over the New Orleans Saints with a pulled left hamstring.
The injury overshadowed a workmanlike win for Dallas (12-3), which already has clinched the NFC East title and the second spot in the conference playoffs behind San Francisco.
Team owner Jerry Jones said it was unlikely that Smith will be available for Saturday's game against the Giants.
The Cowboys have a bye for the first weekend of the playoffs. Smith would have nearly three weeks to recover if he skips the game at New York.
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