CSKA coach Leonid Slutsky explained that the decision was made because of the limit on foreign players.
"We hope that the position of right-back will be taken by a player with a Russian passport. Because of the limit on foreign players, that is the most effective."
Odiah, 27, joined the club in 2004 from Sherrif Tiraspol, and helped them to two League titles, five Russian Cup triumphs and the Uefa Cup in 2005.
But the player has struggled to regain his best form since suffering an anterior cruciate ligament injury playing for Nigeria at the Africa Cup of Nations.
He recently had surgery for a shoulder problem, but has failed to regain his place in the CSKA first team, making just three appearances this season.