The fans have been angry at the Russian FA's decision to stage the June 1 final in the volatile North Caucasus region.
"We're calling on all our supporters to refrain of going to Grozny. Let others follow orders and do what they are told, not us," the CSKA fanclub said in a statement posted on its official website.
"Idiots in the RFU had made a decision to hold the Cup final in a city where local referees and security officials beat up players from visiting teams and the region's head makes public insults and then boasts about it social media."
Last month, Chechnya's strongman leader Ramzan Kadyrov, who serves as honorary president for local side Terek Grozny, insulted referee Mikhail Vilkov over a loudspeaker, calling him a "donkey" after he red-carded his team's captain.
Later that month, Chechen linesman Musa Kadyrov was banned for life for assaulting a visiting player in a reserve game in Grozny when he dropped his flag and ran on to the pitch, attacking startled defender Ilya Krichmar.
In Nov. 2011, Krasnodar striker Spartak Gogniyev suffered a broken nose and fractured ribs after being attacked by Terek officials at a reserve game in Grozny.
Gogniyev was given a six-game ban and fined $1,600 for pushing the referee. The world players' union FIFPro criticised the decision to punish the player.
"By boycotting the final we want to express our outrage by the stupid decision of the RFU, totally ignoring the fans' opinion," the statement said. "We're still asking all our followers to boycott all the away games played in the Caucasus."
The boycott threat was the latest in a series of soccer-related incidents between ethnic Russians and those from the Caucasus regions, such as Chechnya and Dagestan, where wealthy Anzhi are based.
Last year, Dagestan leader Magomedsalam Magomedov appealed to the Russian people to fight nationalism and racism after a Europa League match between Anzhi and Dutch club AZ Alkmaar in Moscow was marred by crowd trouble.
Some Moscow fans were pictured giving a Nazi salute and chanting slogans such as "Russia is (only) for Russians" and "Caucasians go home".
Magomedov said then it was not the first time Anzhi fans had been victims of nationalistic violence.
Last August, police in St Petersburg opened a criminal case after several Anzhi supporters were attacked by local fans in Russia's northern capital.
Several Zenit St Petersburg supporters said they were badly beaten by police and stadium security staff after a league game against Anzhi in Makhachkala last August.
- Sports & Recreation
- Terek Grozny
- Ramzan Kadyrov