"I feared for my life," Nikezic, 29, was quoted as saying by local media on Tuesday.
The forward added that he was invited into a room at the training ground last week and was met by "two strong men."
"After I had initially refused to annul my contract, one of the men punched me while the other took off his jacket and I saw he had two guns," Nikezic said.
"Then I was punched again. The whole thing lasted about 20 minutes. I was scared and agreed to sign whatever they asked."
Kuban, promoted to Russia's top flight after winning the division one title last year under former Chelsea full-back Dan Petrescu, have strongly denied the allegations.
Nikezic, who represented Serbia and Montenegro at the 2004 Athens Olympics, said he had written to FIFA president Sepp Blatter and UEFA chief Michel Platini, asking for help.
A FIFA spokesman said: "We are seeking to verify whether FIFA has officially received any correspondence in relation to the player Nikola Nikezic."
Nikezic was quoted in the Kommersant daily as saying: "I signed a two-year contract with Kuban in March 2010 and helped them win promotion to the Premier League last year."
"This year, however, I was told the club didn't need me any more, offering to break up the contract, but I refused."
The Russian FA (RFS) said they would investigate the allegations and Kuban general director Suren Mkrtychan told Reuters in a telephone interview from Krasnodar:
"Yes, we're aware of the RFS investigation. We'll assist the RFS, FIFA, UEFA or anyone else to find the truth.
"We'll also take all the necessary legal steps to protect ourselves from such a slander."
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