The influential defender missed Saturday's Barclays Premier League win at West Ham, and Belgium's recent World Cup qualifiers, after suffering a thigh injury against Everton earlier this month.
Manager Manuel Pellegrini said there was a possibility the 27-year-old could return to face the Russian champions this week, but he has now decided against the risk ahead of Sunday's trip to Chelsea.
Midfielder Jack Rodwell, who is reportedly fit again after overcoming his latest hamstring issue, has also not been included in the squad for the Group D fixture.
Centre-back Martin Demichelis, who has not featured since being signed in August due to a knee injury, is close to fitness but the game comes too soon.
Winger Jesus Navas, who was not involved at West Ham, has travelled for the crucial game.
After defeat to Bayern Munich last time out, City's hopes of reaching the knockout stages for the first time could hinge on their upcoming back-to-back matches against CSKA.
The two sides are level on three points, three behind Bayern, after recording victories over Viktoria Plzen but losing to the reigning champions.
Pellegrini, who took Villarreal to the semi-finals of the competition in 2006, is in confident mood.
The Chilean told City Today: "I don't think we are going to lose in Moscow. I suppose it happens - (and) also we can qualify - but we are not going to lose in Moscow."
There had been concerns over the state of the pitch at the Arena Khimki after CSKA moved their last home group match against Plzen to St Petersburg.
Heavy rain ruined an already worn surface but, after remedial work, UEFA passed it fit a fortnight ago.
Speaking after the game at West Ham, Pellegrini said: "We don't know what the condition of the pitch will be.
"We hope that UEFA allowed them to play the game there because it is a good pitch."
- Sports & Recreation
- Manuel Pellegrini
- Barclays Premier League
- Jack Rodwell
- Martin Demichelis