We develop a supersymmetric extension of the Susskind-Polychronakos matrix theory for the quantum Hall fluids. This is done by considering a system combining two sets of different particles and using both a component field method as well as world line superfields. Our construction yields a class of models for fractional quantum Hall systems with two phases U and D involving, respectively N₁ bosons and N₂ fermions. We build the corresponding supersymmetric matrix action, derive and solve the supersymmetric generalization of the Susskind-Polychronakos constraint equations. We show that the general U(N) gauge invariant solution for the ground state involves two configurations parameterized by the bosonic contribution k₁ (integer) and in addition a new degree of freedom k₂, which is restricted to 0 and 1. We study in detail the two particular values of k₂ and show that the classical (Susskind) filling factor ν receives no quantum correction. We conclude that the Polychronakos effect is exactly compensated by the opposite fermionic contributions.