"Karpin has been appointed Spartak's caretaker coach until the end of the year," the club's spokesman Alexei Matveyev told Reuters.
The club will then search for a new coach during the Russian winter break.
Karpin had a distinguished playing career with Spartak and Spanish clubs Valencia, Real Sociedad and Celta Vigo but had no coaching experience before becoming general director at the Moscow club in August 2008. Eight months later he fired Denmark's Michael Laudrup as coach and took over the hot seat.
Spartak, Russia's most successful and popular club with nine league titles between 1992 and 2001, have not claimed any domestic trophies since winning the Russian Cup in 2003.
Sunday's defeat left them in seventh place, 10 points behind leaders CSKA Moscow, who take on Zenit later on Monday.
