"The club's personnel and security services at the stadium have been working hard so that the players and fans alike would enjoy tomorrow's match," the Russian champions said on their website on Wednesday.
"Zenit have always condemned any form of racism. We hope our opponents share the same principles and tomorrow we all be treated to a great football match and passionate crowd support."
Zenit supporters have been notorious for racist chanting during home games while the city of St Petersburg is known to have a strong right-wing nationalist influence.
In December, Zenit's largest fan group demanded the club refrain from buying black and gay players following turmoil surrounding the acquisition of Brazil striker Hulk. The fans said they want more home-grown or European players in the team.
Zenit are the only top club in Russia to have never signed an African-born player.
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