The Croatia international sustained a calf problem against Borussia Dortmund at the weekend and has been replaced in Bayern's squad by 18-year-old Julian Green.
Mandzukic played 56 minutes of the Bavarians' 3-0 win at BVB on Saturday before being replaced by Mario Gotze, who went on to score the opener on his return to Signal Iduna Park.
Pep Guardiola's side heads into the Group D clash having already qualified for the round of 16 with four wins from as many games and another three points on Wednesday will seal top spot if Manchester City slips up at home to Viktoria Plzen.
CSKA will hope that home advantage can help the club secure third place and Europa League football in the new year.
Mandzukic has scored 10 goals in 19 appearances this season, while his replacement, American-born Green, has netted 15 times in 18 outings for Bayern's reserve team and could make his professional debut.