The 23-year-old defender limped off with an ankle injury during the goalless draw against Millwall.
"Jack has a kick that has hit him on the nerve, that is the early prognosis," said Forest boss Stuart Pearce.
"If that is the case, then good. But we will not rush him back too quickly.
"We will make sure he is right when he does come back, because he has been a big player for us this season. He has been outstanding, he gives us a real outlet on the right side with his delivery."
Hunt is on loan at Forest from Crystal Palace until the New Year.