The Giants receiver has a partially torn pectoral muscle and won't play against the Cowboys.
Also ruled out are C Shaun O'Hara (foot), OL David Diehl (hip/hamstring), FB Madison Hedgecock (hamstring) and KR/PR Darius Reynaud (hamstring). OL Will Beatty (foot) is questionable after doing some work today.
Tom Coughlin said Smith, who suffered the injury in practice on Thursday, will not need surgery.
"It's going to be one of those deals, hopefully it's week to week," Coughlin said. "They say it's a limited amount of time, but not necessarily right away -- this week, or next week. He hasn't had a lot of swelling in there."
Without Smith, the Giants' leading receiver in 2009, Mario Manningham becomes the other starting wideout with Hakeem Nicks. Ramses Barden and Duke Calhoun, who have played sparingly in the offense, will also have bigger roles.
"Mario's going to step up, Ramses is going to step up. Those guys have to come prepared to play," Nicks said. "We'll see how defenses approach us now."