In a short video published on their Twitter account, the club showed three black players, including Brazilian striker Luiz Adriano, doing drills at a training camp in Dubai.
"Look at how the chocolates are melting under the sun," the video's caption said.
Russia has pledged to crack down on racism as the country faces increased scrutiny ahead of this year's World Cup.
"For Russia's biggest club to tolerate and then celebrate racist references of this kind is wrong," said Piara Powar, the head of European anti-discrimination organisation Fare network, in comments carried by the BBC.
Spartak could not be immediately reached for comment.
But in a subsequent tweet on Spartak's Twitter page, Brazilian midfielder Fernando said in a video message: "There is no racism at Spartak. We are a united family."
Spartak Moscow have been fined on several occasions for their fans' racist behaviour.
European soccer's governing body UEFA opened disciplinary proceedings against Spartak youth player Leonid Mironov last month after he allegedly racially abused Liverpool's Rhian Brewster.
The World Cup will be held from June 14 to July 15 across 12 venues in 11 cities including Moscow, St Petersburg and Sochi.
(Reporting by Gabrielle Tétrault-Farber; Editing by Ken Ferris)
