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.
In-form Sergio Aguero, who scored two goals against West Ham at the weekend, was on the plane along with Yaya Toure and Joe Hart.
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.
City have failed to get out of the group phase of the Champions League for the past two seasons and Aguero is aware of the importance of the game against CSKA.
"We have to win, don't we?" Aguero told City TV. "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."
Manuel Pellegrini's men may struggle, however, to repeat their performance in Saturday's 3-1 win at West Ham in Russia with ongoing concerns over the state of the pitch in the capital.
UEFA sent a group of experts to inspect the pitch at CSKA's Arena Khimki after the Russian side were forced to play their last Champions League game against Viktoria Plzen in St Petersburg.
Part of the surface at the stadium, which is CSKA's temporary home while the Luzhniki Stadium is being rebuilt for the 2018 World Cup, had to be relaid after heavy rainfall rendered it unplayable.
"We don't know what the condition of the pitch will be," Pellegrini said. "We hope that UEFA allowed them to play the game there because it is a good pitch."
CSKA Moscow v Manchester City is live on Sky Sports 2 HD on Wednesday afternoon from 4.30pm.