The decision comes following the Serie A strugglers' 3-1 defeat to Fiorentina last weekend, which left the team on the verge of demotion.
Youth team coach Andrea Manzo will be in charge during the crucial Inter decider.
"We give our thanks to Cuper and his assistant Gustavo Siviero for the intense work that they undertook with competence and commitment," a Parma statement read.
"The squad will be put in the hands of Andrea Manzo, Parma’s youth team Coach who will take charge of the game against Inter on May 18."
Parma need a miracle to avoid relegation as they face holders and current leaders Inter with no option but to win the game.
However, the Ducali must make sure relegation rivals Catania lose at home against Roma, who also vie with Inter for the Scudetto.
Cuper, a former Inter manager, is the 13th coach to get the axe in Italy this season.