City moved up to second place in the Championship with the 2-1 home win over Southampton in midweek but the victory came at a price with the duo struggling to be fit to face the Potters.
Carey broke his nose just before the half-hour mark on Wednesday evening while Noble hobbled off before the break with a leg injury.
Carey looks certain to miss out so Jamie McCombe is set to continue at the heart of defence after replacing his skipper against Saints. Noble's chances of playing look more promising but a late decision will be made on his fitness.
Johnson said: "It is going to be hard for Louis to play on Saturday given the time until then.
"We wanted to give Noble a chance to play on in the second half but he couldn't continue. We will monitor him before the game."
Striker Richard Cresswell will be the main absentee for Stoke.
Cresswell, who netted a brace in the 3-1 win at Crystal Palace in midweek, will miss the game as he serves a one-match ban after amassing his fifth booking of the season against former club Sheffield Wednesday last weekend.
Boss Tony Pulis, who briefly managed at Ashton Gate between July 1999 and January 2000, is still without forward Mamady Sidibe (gashed arm) but is boosted by the availability of Vincent Pericard.
The former Juventus striker was been released from prison on Wednesday and will travel with the squad but it remains to be seen whether the 25-year-old is deemed match fit.
Ricardo Fuller is struggling with a combination of a dead-leg and an ankle injury but should feature while Demar Phillips is still waiting to make his City bow after being an unused substitute in the last few games.
Clint Hill is also nearing full fitness after suffering a damaged rib last month and could be pushing to be involved while Stephen Wright is fit again after overcoming a calf problem.