The side have not won in the league since January 20, and their 7-0 defeat to Manchester City was their fifth in a row in all competitions.
After the defeat at the Etihad, Tedesco denied that he would resign, saying: "I haven't given a second thought to changing anything on my side. I am proud, even now, to be coach of Schalke 04. Even in these difficult times, I like being here and giving my all."
He leaves the German side 14th in the Bundesliga table, with Huub Stevens and Mike Buskens taking charge of the club's next game, which will be against RB Leipzig this weekend.