It is unknown how long McNabb will be sidelined, but Reid said "there's a chance" he would play next week against the New Orleans Saints.
McNabb will be examined further on Monday after the team returns to Philadelphia.
McNabb scored on a 3-yard run in the third quarter to give the Eagles their final margin of victory. He didn't immediately get up after the touchdown, and was attended to by Eagles trainers before eventually leaving the field on his own.
While he was on the ground, quarterback Michael Vick was captured on TV standing in a stadium suite to watch McNabb. Vick is suspended for the first two regular-season games to complete penalties for bankrolling a dogfighting ring.
McNabb was replaced by Kevin Kolb, who would be in line to start at quarterback in Week 2 against New Orleans.
Meanwhile, after reviewing the hit on McNabb, the NFL has determined there was nothing illegal about the play and Panthers defensive linemen Damione Lewis and Tyler Brayton -- who fell on top of McNabb -- will not be fined, ESPN NFL Insider Adam Schefter reports.
ESPN's Sal Paolantonio and The Associated Press contributed to this story.