Anzhi said on their website on Saturday that Tuesday's last-16 tie in Makhachkala, the capital of largely Muslim Dagestan, had been switched to the Chechen capital of Grozny.
The club, who signed former Brazil and Real Madrid left-back Carlos this month, did not give further details. Local media reported the game was moved because of the escalation in violence in the area.
On Friday, militants simultaneously attacked several strategic points in the region, where Moscow is battling an Islamist insurgency.
Officials for Anzhi and Russian champions Zenit were unavailable for comment on Saturday.
Roberto Carlos's arrival has raised Anzhi's profile one month after the club was bought by Russian billionaire Suleiman Kerimov.
Terek Grozny, a club run by the Chechen leader Ramzan Kadyrov, have also been in the spotlight recently, after they named former World Player of the Year and Dutch international Ruud Gullit as their new coach in January.
