The tweet came from the club's official account and shows Spartak trio Luiz Adriano, Pedro Rocha and Fernando stretching in the United Arab Emirates sunshine.
Spartak later posted a video in which Fernando says: "At Spartak there is no racism".
Spartak had seemingly turned its Twitter account over to defender Georgy Dzhikiya for the day.
The original post was then deleted, before the club uploaded a third video with Dzhikiya and the three Brazilians in a group hug. The players had their arms around each other, and Adriano said, "This is my friend, my brother".
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"This shows a shocking level of ignorance. References like this show how some minorities are seen by some in the country", said Piara Powar.
UEFA ordered them to partially close their academy stadium for a fixture after a section of fans were guilty of racist behaviour towards Nigeria-born Liverpool striker Bobby Adekanye.
They are also now being investigated by UEFA over allegations that Reds youngster Rhian Brewster was racially abused during a UEFA Youth League match at the Spartak Academy in Moscow back in December.
"This social media post from the official account of Spartak Moscow only continues to highlight the prejudices towards black people in Russian Federation", read a statement posted on the official Kick It Out Twitter page.
"With the World Cup only a few months away, it is a reminder that Russian Federation - as with the whole of football - has significant work to do to eradicate racism of all forms from the game".
But Russia has vowed to ensure fans' safety when it hosts the 2018 World Cup by cracking down on both hooliganism and racism.