Veteran midfielder Lampard, who has impressed on a six-month loan spell from New York City FC having left Chelsea, was injured making tackle in the first half.
"Frank has a muscle injury," manager Manuel Pellegrini said. "We will see tomorrow after the scan but for the moment he will not travel to Russia."
Lampard earned the penalty for City's second goal.
City have managed only one point from their opening two Champions League Group E games and need to beat bottom-placed CSKA to keep in touch with Bayern Munich and Roma.
(Reporting by Martyn Herman, editing by Ed Osmond)
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