The Croatia international played 56 minutes of Bayern's 3-0 win at Bundesliga rivals Borussia Dortmund on Saturday evening but is still struggling with a calf injury sustained in his country's World Cup play-off victory over Iceland.
In his place, coach Pep Guardiola has handed a first call-up to the senior squad for 18-year-old Julian Green, a United States-born Germany Under-19 international.
Defending champions Bayern have already qualified for the knockout stages and need to better Manchester City's result against Viktoria Plzen on Wednesday to make sure of finishing top of Group D.
President Uli Hoeness told the Bayern website prior to the team's departure for Russia: "(I'd like) at least a point, even better a win.
"Then the starting point for the final game against Manchester City is excellent. We really want to be group winners."