Kompany sustained a thigh injury a fortnight ago against Everton but was expected to return for the Sky Live Group D clash.
However, the Belgian, along with Martin Demichelis (knee) and Jack Rodwell (hamstring), did not travel to the Russian capital with the rest of the squad.
City will be aiming to bounce back from a 3-1 home defeat to group leaders and reigning champions Bayern Munich in their last game.
CSKA are level with City on three points but head into the clash without a victory in their last five league fixtures.
Aguero: "We have to win, don't we?
"It's an important three points because then we play them at home. We won against West Ham away in the Premier League and now we have to win away in Moscow as well.
"It was very important to win against West Ham and now we have to keep winning away matches. We have to continue."
Source: Manchester City MAD