  A novel reduction procedure for covariant classical field theories,
reflecting the generalized symplectic reduction theory of Hamiltonian systems,
is presented. The departure point of this reduction procedure consists in the
choice of a submanifold of the manifold of solutions of the equations
describing a field theory. Then, the covariance of the geometrical objects
involved, will allow to define equations of motion on a reduced space. The
computation of the canonical geometrical structure is performed neatly by using
the geometrical framework provided by the multisymplectic description of
covariant field theories. The procedure is illustrated by reducing the
D'Alembert theory on a five-dimensional Minkowski space-time to a massive
Klein-Gordon theory in four dimensions and, more interestingly, to the
Schr\"odinger equation in 3+1 dimensions.
