The visitors, meanwhile, will be hoping they can help Russia make some impact on the competition after a dismal campaign last season when the country's two sides, Spartak Moscow and Zenit St Petersburg, managed just three wins between them on the way to group stage elimination.
Bayern's treble-winning season was always going to be hard to live up to and there has definitely been an anti-climatic feeling about the start to the new term, despite the arrival of new coach Pep Guardiola.
Even though Bayern have taken 13 points out of a possible 15 in the Bundesliga and won the Supercup, they have been overshadowed by a much more flamboyant Borussia Dortmund team who have won all their league matches and scored 15 goals to Bayern's nine.
Bayern have also suffered with injuries to Javi Martinez and Bastian Schweinsteiger as well as new signings Mario Goetze and Thiago Alcantara.
There was definitely a run-of-the-mill feel to Bayern's 2-0 win over Hanover 96 on Saturday, which angered sporting director Matthias Sammer.
"We played lethargically at times, we played football without emotion, we worked as if we were following rules," Sammer told German media.
"We must get out of our comfort zone. It's nothing to do with lack of effort, we're lacking that last five percent," he added.
Bayern have won 12 of their last 14 home games in Europe, suggesting that Tuesday's Group D match, the first-ever meeting between the teams, could also be something of a formality.
However, Russian champions CSKA have also started the season well and are unbeaten after eight league games.
The former Soviet army club, in the group stage for the seventh time, reached the quarter-finals in 2009/10 under coach Leonid Slutsky, who is still in charge.
CSKA, who spent a modest 10 million euros during the transfer window, suffered a blow at the start of the month when their Ivorian striker Seydou Doumbia was ruled out for around six weeks with a back injury.
But they have reinforced their attack by signing 19-year-old Brazilian Vitinho who made his professional debut for Botafogo this year and quickly turned into their most important player.
Vitinho, however, could find the Champions League a huge step up from the ponderous defences in the Brazilian championship.