The Russians axed Unai Emery on Sunday after a disastrous 5-1 defeat by city rivals Dynamo Moscow.
Ironically, Karpin himself was moved upstairs at the club earlier this year to allow Spanish boss Emery to take his job.
Now the 43-year-old has been handed the reins again until the end of the year to give the Spartak board time to bring in their new man.
And that means the former Real Sociedad and Valencia midfielder will be in the away dug-out at Parkhead for the vital Champions League tie, with Celtic needing to better Benfica's score at Barcelona to qualify for the last 16.
Spartak – who lost 3-2 to Celtic in Russia – are already out of Europe after only claiming three points from five Group G games.