<p>The propagation of magnetosonic, nonlinear monotonic, and oscillatory shock structures in a homogeneous plasma with arbitrary degeneracy of electrons is investigated using a quantum magneto-hydrodynamic model (QMHD). The ions are classical, and dissipation in the system is taken through their kinematic viscosity. The electrons are degenerate, and their quantum effects through Bohm potential term are included. The reductive perturbation method is used to study the energy transfer mechanism, and the nonlinear Korteweg–de Vries–Burgers (KdVB) equation is derived for arbitrary degenerate plasmas. The different solutions of the KdVB equation are presented for monotonic and oscillatory shock structures in the presence of degeneracy of electrons. The effects of chosen values of equilibrium fugacity, electron temperature, magnetic field, and the corresponding electron density of a physical quantum plasma system on the height (intensity) of the monotonic and oscillatory shock structures are pointed out. These findings may be helpful to understand the excitation of magnetosonic shock wave phenomena in astrophysical, space, and fusion plasmas.</p>