"We're not racists but we see the absence of black players at Zenit as an important tradition," Zenit fan club Landscrona said in a letter, called the "Selection 12 manifesto", posted on its website on Monday.
"It would allow Zenit to maintain the national identity of the club, which is the symbol of St Petersburg."
Zenit have been the only top club in Russia to have never signed an African player while the northern city of St Petersburg is known to have a strong right-wing nationalist influence.
The fans said they want more home-grown or European players in the team.
"We only want players from other brotherly Slav nations, such as Ukraine and Belarus as well as from the Baltic states and Scandinavia. We have the same mentality and historical and cultural background as these nations," the letter said.
They also expressed their opposition to having "sexual minorities" in the team and demanded that each player would give "101 percent effort" in every match.
Several prominent black players have turned down lucrative offers from the wealthy club over the past 12 months after receiving death threats from Zenit fans, local media reported.
A Zenit spokesman said on Monday the club would not comment on the fans' letter.
Former Zenit and Russia striker Alexander Panov said the fans have no right to influence the club's selection policy.
"If we don't have enough good players from St Petersburg, then what should the club do?" the St Petersburg native was quoted as saying by local media.
"All clubs around the world have black players. If they are absent from Zenit - it's Zenit's problem. I don't think fans should demand the club buy or don't buy certain players. The fans have the right to go to the stadium or stay home."
Zenit have been in turmoil for the past few months with several senior players unhappy after the wealthy club splashed out more than $100 million on Brazilian Hulk and Belgium midfielder Axel Witsel just before the transfer deadline.
Zenit demoted Russia skipper Igor Denisov to the reserve team in September after he refused to play, issuing an ultimatum to renegotiate his contract in line with what Hulk was making.
Denisov was later allowed to rejoin the first team after making an apology.
