Local newspapers published a picture of a fan offering a banana to Anzhi captain Roberto Carlos at St Petersburg's Petrovsky stadium before Monday's match which Zenit won 2-0.
"In regards to a published photo of a man making an unethical act towards Anzhi captain Roberto Carlos, Zenit officially state that the club together with the police will investigate this matter," Zenit said on their website.
Roberto Carlos himself played down the incident.
"I didn't get offended," the 2002 World Cup winner who joined Anzhi from Brazilian club Corinthians last month, was quoted as saying by Russian media. "In my 37 years I've seen it all so I didn't get upset after seeing a banana."
The Russian FA said it was also investigating the incident.
If found guilty, Zenit could be fined, forced to play home games behind closed doors or have points deducted.
It was the latest in a series of racist incidents in soccer in recent years in Russia, which will host the 2018 World Cup.
Nigeria striker Peter Odemwingie, who left Lokomotiv Moscow to join English Premier League side West Bromwich Albion last year, was the subject of similar abuse from Russian fans, who unfurled a racist banner celebrating his departure.
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