It is said the Premier League club lodged a complaint to European football's governing body after Bobby Adekanye was allegedly the victim of racist abuse.
UEFA confirmed on Wednesday that the Russian club is facing disciplinary proceedings, specifically relating to claims that "monkey chanting" was heard.
The case will be heard by the UEFA Control, Ethics and Disciplinary Body on October 19.
Spartak were also charged last month for breaching regulations concerning illicit banners, the setting off of fireworks and for blocking stairways during the senior side's 1-1 Champions League draw with Liverpool.
That case will also be heard in two weeks' time.
They were previously fined €60,000 and banned from selling tickets to supporters for their next away match in the competition following a firework incident during their opening group game against Maribor.