<p>A rigorous theoretical investigation has been made on the propagation of nonlinear gravito-nucleus acoustic waves (shock waves) in a magnetized degenerate quantum plasma, whose constituents are noninertial degenerate electrons and inertial nondegenerate heavy nuclei. To study the nonlinear propagation of these shock waves in the plasma system under consideration, the well-known reductive perturbation technique is used. The Burgers equation is derived and the associated shock structure solution is obtained to analyze the shock profile numerically. The dissipative force is responsible for the formation of the gravito-nucleus acoustic waves (GNAWs). The basic properties (amplitude, width, steepness, etc.) of these GNAWs have also been studied, which are significantly modified by the variation of kinematic viscosity, obliqueness, and number density of the plasma species. The results obtained from our present investigation can be applied to astrophysical compact objects like white dwarfs and neutron stars.</p>