Vick sustained the injury early in the second quarter of the Eagles' 38-23 loss to Dallas Sunday after absorbing two hits by Cowboys defenders.
Rookie Nick Foles made his first NFL appearance during the game and is now likely to get his first start next week against the Washington Redskins after Reid told reporters Vick was still "foggy" after the game.
Reid said Vick had a "significant concussion" and will go through the medical protocol for assessing the injury, thus delaying a possible return to practice.
"He's resting right now," Reid said. "[In] this period, it's very important that he rests."
The injury came as more bad news for the struggling Eagles, who fell to 3-6 with their fifth straight loss.