Abstract <p> The path integral reduction procedure—a transformation describing the transition from an original Wiener-type path integral to a path integral for a reduced dynamical system—is extended to path integrals of a special mechanical system with symmetry, considered as a model for the Yang–Mills field interacting with a scalar field. The mechanical system is defined on a smooth compact Riemannian product manifold consisting of the total space of the principal fiber bundle and a vector space. The original manifold is endowed with a free, proper, and isometric action of a compact semisimple Lie group. The factorization of the path integral measure within the reduction procedure is based on using the optimal nonlinear filtering equation from stochastic theory. For the reduction of the system corresponding to the transition to the zero-momentum level, the Jacobian of the path integral reduction is obtained. Its geometric representation follows from the formula for the scalar curvature of a manifold with the Kaluza–Klein metric. An integral relation between the path integrals representing the fundamental solutions of the parabolic equations on initial and reduced manifolds is derived. An example demonstrating the application of the obtained reduction procedure in the path integral to a simple mechanical system is provided. </p>