"Today the board of directors accepted my resignation," Karpin told the club's website. "I was ready to quit my other job as general director but the board did not discuss such a scenario."
Billionaire owner Leonid Fedun said a new coach would be appointed inside two days.
"We'll announce it on Tuesday or Wednesday. I'm doing the negotiations myself," Fedun was quoted as saying by local media.
Karpin's resignation came after Sunday's 2-1 defeat at Anzhi Makhachkala left Russia's most popular club bottom of the table with four points from five games.
It was Spartak's fourth defeat in five matches including a 10-3 aggregate drubbing by Porto in the Europa League quarter-finals.
Eight months later he fired Denmark's Michael Laudrup as coach and took over the hot seat.
Spartak, the country's most successful club with nine league titles between 1992-2001, have not won a major trophy since lifting the Russian Cup in 2003.
