Emery's men were eliminated from the Champions League with a 3-0 defeat to Barcelona in midweek, with Celtic the side's remaining opponents in the competition on December 5.
But despite signing a two-year contract in May, taking over from the club's general director Valery Karpin, a second home thrashing in a week signalled the end for Emery.
Karpin said: "The club's shareholders have taken the decision that Unai Emery will no longer coach Spartak.
"We will announce our next steps soon."
Former Spartak midfielder Yuri Gavrilov told Sport Express: "I do not know what the Spartak leadership is going to do now.
"Not every trainer is going to agree to go there. It's clear that this team, with all its name and history, needs completely different players."
Spartak, who picked up nine league titles between 1992 and 2001, have not claimed any domestic trophies since winning the Russian Cup in 2003.