The former Blackburn Rovers defender was subjected to racist chants throughout a recent fixture between the sides, and had a banana thrown at him.
Speaking in a joint statement, both clubs have promised that the perpetrators will be thoroughly punished for bringing the Russian game into disrepute.
"The common task of the concerned parties to find, and make public the concrete b*****d whose conduct raised concerns about football itself," said a statement released jointly by the two teams.
"Both clubs are confident that the match was organised on a high level, the players played out a brilliant and tense football with vivid emotions and a magnificent atmosphere."But all this was ruined by the conduct of one provocateur. Such people cannot be referred to as fans of football. They have nothing in common with the real supporters of the clubs.
"Both Anzhi and Lokomitiv are determined to identify this person."
Lokomotiv Moscow were 1-0 victors, leaving Anzhi in seventh place in the Russian Premier League table.