Neutron scattering from spatially ordered arrays of magnetic nanowires synthesized inside a nonmagnetic matrix is theoretically described. Expressions for the nuclear, magnetic, and interference contributions to the neutron scattering cross section are obtained. It is shown that, when polarized neutrons are scattered from an array of magnetic nanowires, the scattering cross section is not only a nonlinear function of the nanowire length but also depends on the neutron wavelength. These expressions describe the complex nature of the neutron-diffraction pattern as a factor of the ratio of nuclear and magnetic scattering amplitudes.