Marsch was appointed in the summer on a two-year deal after Julian Nagelsmann agreed to move to Bayern Munich but Leipzig have endured a difficult start to the season.
A 2-1 defeat to Union Berlin on Friday was their third loss in a row and left them 11th on the Bundesliga standings.
Leipzig have also been knocked out of the Champions League and face a fight with Club Brugge so secure the Europa League spot in a group that contains Manchester City and Paris Saint Germain.
Club chief executive Oliver Mintzlaff said: “It was not easy for us to part company with Jesse Marsch, because I hold Jesse in high regard as a person and as a coach.
“It is a shame that things did not work out as we had hoped with this setup, and that this step has now become necessary. Unfortunately, the development we were hoping for and the results needed to achieve our goals for the season have not been achieved.
“We are currently running short of our own expectations and with this decision we want to create a new impulse. Regardless of this, however, I also see our players as having a duty and I expect our team, which is very strong in sporting terms, to show its potential and quality on the pitch more consistently than it has done recently.
“I would like to thank Jesse Marsch for the work he has done and wish him all the best, both personally and professionally.”
Assistant manager Achim Beierlorzer has been placed in a caretaker role until a new manager is appointed.
