"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," Leicester said in a statement.
"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."
Puel had been appointed Leicester manager in October 2017 when they were 14th in the standings and the Frenchman led the club to a ninth-placed finish in his first season.
Although the club were in seventh place at the turn of the year, they had a dismal start to 2019, suffering four consecutive home defeats.
Earlier this month, Peter Schmeichel, father of Leicester keeper Kasper, said the club did not have a manager capable of getting the best out of the players and indicated that his son might be looking to move.
Leicester's Jamie Vardy had also been critical of Puel's style of play this season although Puel said there was no rift with the striker.
Leicester's next game is a league trip to Brighton & Hove Albion on Tuesday.
(Reporting by Rohith Nair in Bengaluru; editing by Sudipto Ganguly and Christian Radnedge)
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