The aim of this paper is to generalize the classical Marsden- Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in or der to obtain quotient manifolds which in- herit the polysymplectic structure. This generalization a llows us to reduce polysymplectic Hamiltonian systems with symmetries, suuch as those appearing in certai n kinds of classical field theories. As an application of this technique, an analogous to the Kirillov -Kostant-Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in pr evious papers [28, 48] on this subject.