Mikel played the entire 90 minutes on Saturday as Trabzonspor beat Fenerbahce 2-1 in a charged league game to climb above their opponents into third place on the table.
The former Nigeria captain clashed with Fenerbahce midfielder Emre Belozoglu after the game and the pair had to be separated by teammates.
Mikel’s social media accounts was thereafter inundated with abusive messages to him and his family.
The Turkish club said in a statement: "Racism is a refuge for helpless and ignorant people. Our football player, Obi Mikel, condemns the racist attacks after the Fenerbahce match.
"We present to the public that we have filed a criminal complaint against the attackers."
Mikel's team-mate Joao Pereira also said on Twitter: "It is sad and unacceptable that in 2020 we're still facing acts of racism and disrespect like this. Football is much bigger than the little people behind these unfortunate acts."
Mikel joined Trabzonspor on a free transfer in the summer and has gone on to make 22 appearances in all competitions.
The former Chelsea midfielder won two Premier League titles and the Champions League during his time at Stamford Bridge, and he also helped Nigeria win the Africa Cup of Nations in 2013.
