The USA international was forced off in the second half of Celtic's 3-0 win at Dundee on Boxing Day due to "tightness" in his hamstring.
Rodgers was initially hopeful that Carter-Vickers would be fit for the club's upcoming fixtures, but Saturday's game will come too soon for the defender.
Speaking at a press conference on Friday, Rodgers said: "[Carter-Vickers] will not be available for the next two games.
"It's not longer term, but you probably won't see him until after the winter break."
Carter-Vickers was also injured for the first Old Firm derby of the season back in September when Celtic claimed a slender 1-0 victory over Rangers at Ibrox courtesy of a first-half goal from Kyogo Furuhashi.
Stephen Welsh replaced Carter-Vickers at Dens Park in midweek and the 23-year-old is in contention to start at centre-back for the Hoops on Saturday.
"Stephen came in against Feyenoord and played very, very well," said Rodgers. "I've really like seeing him, I brought him with me as a young player when I was here the first time around, and he was only a kid then but he's really matured.
"Maybe he hasn't played so much as he would've liked, but only because of the form of Cam (Carter-Vickers) and Carl Starfelt when he was here, so that was the challenge for him.
"But he's always there as a loyal support to play and I know that I can trust him when I put him in, so if he's the guy that gets the chance to play, then I've got every faith that he can perform."
Carter-Vickers will join James McCarthy (hamstring) in the treatment room, but winger Liel Abada (thigh) and midfielder Reo Hatate (hamstring) could return to matchday squad following lengthy spells on the sidelines.
While Abada last featured for Celtic in the aforementioned win at Rangers almost four months ago, Hatate has been sidelined for the last two months but has since returned to training.
Celtic enter Saturday's contest sitting five points clear at the top of the Premiership table, but Rangers, who boast a 16-game unbeaten run in all competitions under new manager Philippe Clement, have two games in hand on the Hoops.
"[Old Firm derbies] are amazing games," said Rodgers. "It's such an iconic game to be involved in and obviously we got a great result at Ibrox earlier on in the season, and now we're in front of our own supporters, were really excited by it.
"It's a fantastic game to be involved in, the atmosphere will be electric tomorrow and that's what I really can't wait for. But it's up to us to again provide that urgency and intensity to win the game."
Celtic will be confident of success in front of a sellout crowd at Parkhead as they have only lost one of their last 11 meetings with Rangers, winning their last two on home soil by an aggregate score of 7-2.