The 36-year-old left the field on a stretcher after going down hurt during the first half of City's 4-1 Barclays Premier League win over Tottenham at the Etihad Stadium.
Lampard will now have a scan to determine the seriousness of the problem but there seems little prospect of him being involved in Tuesday's Champions League Group E game in the Russian capital.
Manager Manuel Pellegrini said: "Frank has a muscle injury
We will see on Sunday after the scan but for the moment he will not travel to Russia."
Lampard, who was released by Chelsea at the end of last season, has made a big impression at City since joining the club on loan from sister club New York City
He is due to link up with the American side to prepare for the 2015 Major League Soccer season in the new year.
Source : PA
Source: PA