The move was made in the wake of yesterday's thumping by Crystal Palace.
Leicester said in a statement:
King Power Stadium
"The Club would like to thank Claude for his efforts in leading the team during his 16 months in the role and wish him well in his future career.
"Assistant Manager Jacky Bonnevay also departs with the Club's best wishes.
"First Team Coaches Mike Stowell and Adam Sadler, supported by the Club's established backroom staff, will assume responsibility for the senior squad while the Club begins the process of appointing a new manager.
"The Board will make no further comment until this process is complete."