Leeds said in a statement: “We would like to thank Jesse and his backroom staff for their efforts and wish them well in the future.”
“The process of appointing a new head coach is underway and we will continue to keep supporters up to date in the coming days.”
Leeds have won only four of their 20 league matches this season, losing 10 and drawing six.
The 49-year-old Marsh has taken a total of 11 wins in his 37 matches and his team last won a league match on 5 November when they beat Bournemouth 4-3.