The 30-year-old Neuer had a tight calf and would stay in Munich for treatment, with Sven Ulreich taking his place, CEO Karl-Heinz Rummenigge said.
Robben has yet to recover from a muscle injury picked up while on international duty with Netherlands last week.
Bayern coach Carlo Ancelotti will also be without injured Javi Martinez, Arturo Vidal and Kingsley Coman for Wednesday's Group D encounter.
Bayern, who were beaten 1-0 by domestic rivals Borussia Dortmund in the Bundesliga on Saturday, have already qualified for the knockout stages of the Champions League and are second in their group on nine points from four games.
"If we win then we can theoretically still have a chance to top the group ahead of Atletico (Madrid)," Rummenigge told reporters.
Spain's Atletico lead the group on 12 points, while Rostov and Dutch side PSV Eindhoven have one point apiece with two games to play.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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