The Foxes dropped into the relegation places with a 2-1 defeat by Crystal Palace on Saturday.
Rodgers was appointed in February 2019 and led the club to its first FA Cup triumph in 2021.
But in a statement, chairman Aiyawatt Srivaddhanaprabha said performances and results this season have been “below our shared expectations”.
“It had been our belief that continuity and stability would be key to correcting our course, particularly given our previous achievements under Brendan’s management,” he added.
“Regrettably, the desired improvement has not been forthcoming and, with 10 games of the season remaining, the board is compelled to take alternative action to protect our Premier League status.
“The task ahead of us in our final 10 games is clear. We now need to come together – fans, players and staff – and show the poise, quality and fight to secure our position as a Premier League club.”
Rodgers led Leicester to consecutive fifth-place finishes in his first two full seasons as Foxes boss, as well as beating Chelsea to lift the FA Cup in 2021.
But his side began the 2022-23 campaign with seven defeats from their opening 10 Premier League games, slumping to the bottom of the table before a run of four wins from five games going into the World Cup break.
They have struggled since the season resumed, however, collecting just seven points from 33 available.