A video posted on the club's Twitter account showed Brazilian players Luiz Adriano, Pedro Rocha and Fernando exercising during a training camp in the United Arab Emirates. A message which translated as "see how the chocolates melt in the sun" accompanied the video, followed by three emojis of a smiley face.
The same phrase is heard during the video, apparently spoken by Spartak and Russia defender Georgy Dzhikiya. Spartak earlier said Dzhikiya would take control of its Twitter feed for the day.
Spartak later posted a video in which Fernando says: "At Spartak there is no racism. We are a friendly family."
The original post was then deleted, before the club uploaded a third video with Dzhikiya and the three Brazilians in a group hug.
"We're all one big family," Dzhikiya said, before Luiz Adriano added: "This is my friend, my brother ... a legend of Spartak. I love you, my friend."
Russia is hosting the World Cup in June.
Anti-discrimination group the FARE Network, which investigates racism issues for UEFA, criticized Spartak.
"This shows a shocking level of ignorance. For Russia's biggest club to tolerate and then celebrate racist references of this kind is wrong," FARE executive director Piara Powar said in a statement. "Racism is one of the biggest issues Russia faces in the year they host the World Cup, references of this kind show how some minorities are seen by some people in the country."
Spartak player Leonid Mironov is already facing a UEFA racism charge over alleged racist abuse of Liverpool's Rhian Brewster during a Youth League game in December. Mironov denies any racist comments and has claimed Brewster made up the incident so he would be banned.
Spartak was ordered to close part of its stadium for another Youth League game after UEFA ruled its fans abused Liverpool striker Bobby Adekanye with monkey chants.
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