Tedesco has paid the price for the club's poor recent run with last season's Bundesliga runners-up struggling in 14th, just four points off the relegation zone.
His dismissal was announced by Schalke's director of sport Johan Schneider, who has only been in his post for a week.
"We obviously can't ignore that our progress is very negative. When I took over this role I requested reversing this trend, something which is absolutely necessary given our serious situation in the Bundesliga," he said.
The 33-year-old Tedesco had ruled out resigning after Tuesday's Champions League rout, the biggest European defeat in the club's history.
The drubbing brought the number of goals leaked by Schalke to 21 in the last five games.
Former manager Huub Stevens has been appointed caretaker coach for Saturday's Bundesliga date with RB Leipzig.
The Dutchman coached Schalke between 1996 and 2002, and again between 2011 and 2012.