Spartak part company with Karpin
Since the resumption of the league following the mid-season break, Spartak have failed to beat the two sides at the bottom of the table.
A 1-0 loss at Terek Grozny was followed by a 2-2 draw at home to bottom club Anzhi on Monday.
Those results have left Spartak four points adrift of top spot, with city rivals Lokomotiv Moscow currently leading the way at the summit.
"Today FC Spartak Moscow and head coach Valery Karpin parted company by mutual consent," read a statement on the club's official website.
"Led by Valery, who worked with the team since April 2009, Spartak twice - in 2009 and 2012 - finished runner-up in the championship."
Karpin initially took charge of Spartak in 2009, before relinquishing the position to Unai Emery in May 2012, only to return to the post when the Spaniard was dismissed in November that same year.