Leeds lost 1-0 at Nottingham Forest on Sunday, their seventh Premier League game without a win.
They are 17th in the table – above the relegation zone only on goal difference – and last won in the league on 5 November.
Leeds finished 17th last season after American Marsch succeeded Marcelo Bielsa in February.
A club statement read: “We would like to thank Jesse and his backroom staff for their efforts and wish them well for the future.
“The process of appointing a new head coach is under way and we will continue to keep supporters up to date throughout the coming days.”
Coaches Rene Maric, Cameron Toshack and Pierre Barrieu have also been sacked.
Leeds play Manchester United at Old Trafford on Wednesday and again at Elland Road on Sunday.
Marsch’s side won only four of their 20 league matches this season, with six draws and 10 defeats.
Defeat by Nottingham Forest in his final match in charge left him with a 25% win-rate after 32 Premier League games as Leeds boss.
A former coach of RB Leipzig, New York Red Bulls and Red Bull Salzburg, he took over with Leeds 16th in the table.
They avoided relegation to the Championship thanks to a 2-1 win at Brentford on the final day of last season.