Hart paid the price for a number of high-profile mistakes as he was dropped for Costel Pantilimon for Saturday's Barclays Premier League game against Norwich.
The 26-year-old had to watch as City recorded a comfortable 7-0 win and Pellegrini will not reverse the change for the midweek clash with the Russians.
Pellegrini said: "I don't know when Joe will come back to the team.
"It is very important for him to have a rest. He has played all the matches in the last two and a half years.
"We will see in the future what we must do. For today, Pantilimon is playing."
City will also be without striker Stevan Jovetic for the fixture, with the Montenegro international ruled out for another three weeks.
Jovetic, who has been hampered by injuries since signing from Fiorentina in the summer, was substituted after just 10 minutes of last week's Capital One Cup tie at Newcastle with a calf problem.
Captain Vincent Kompany also remains on the sidelines as he continues his recovery from a groin injury.
Pellegrini said: "Jovetic has at least three weeks (out). Except Vincent Kompany and Richard Wright, all the other players are fit."
Pellegrini dismissed concerns over striker Alvaro Negredo's fitness, saying the Spaniard was substituted early against Norwich after feeling the effects of playing extra time at Newcastle.
He said: "Alvaro is okay, he doesn't have any problem. He just played 45 minutes because he played 115 minutes three days before."
A City victory against CSKA in their fourth Group D match would all but guarantee a place in the knockout stage of the competition.