Dyche has been in charge at Turf Moor since 2012, leading them to two Premier League promotions.
But this season they are in a relegation fight, four points from safety with just eight games to go.
They have lost five of their last six top-flight games, including a 2-0 defeat to Norwich last week.
Assistant manager Ian Woan, first-team coach Steve Stone and goalkeeping coach Billy Mercer have also left the club.
Chairman Alan Pace said: “Firstly, we would like to place on record our sincere thanks to Sean and his staff for their achievements at the Club over the last decade.
“During his time at Turf Moor, Sean has been a credit both on and off the pitch, respected by players, staff, supporters, and the wider football community.
“However, results this season have been disappointing and, while this was an incredibly difficult decision, with eight crucial games of the campaign remaining, we feel a change is needed to give the squad the best possible chance of retaining its Premier League status.
“The process of replacing Sean has begun and further announcements will be made to supporters in due course.”
Dyche famously led Burnley to the Europa League in 2018, the club’s first taste of European football in 51 years.
That followed after a career-best seventh-placed finish in the Premier League for Dyche.
Burnley came 17th last season, one place above the drop, but did so with 11 points to spare.
They find themselves fighting for safety again and travel to West Ham on Sunday, doing so without Dyche in charge for the first time in a decade.
No serious contenders have been linked with succeeding Dyche.
But oddsmakers have named Sam Allardyce as favourite, with former Burnley defender and current Cheltenham boss Michael Duff second favourite at 5/1.
Nuno Espirito Santo and Wayne Rooney are locked together at 12/1, while ex-Toffees chief Rafa Benitez is offered at 16/1.
Burnley still have Southampton, Wolves, Watford, Aston Villa twice, Tottenham and Newcastle still to play after the Hammers.
Dyche was the Premier League’s longest-serving manager, but becomes the tenth coaching casualty of the season.
