The modifications, which arise from ultra-relativistic and degenerate effects of electrons and positrons as well as the chemical potentials in the basic features of three-dimensional isothermal ion acoustic shock waves (IIASWs) propagating in magnetized electron–positron–ion (e–p–i) plasmas are studied. The cold ions are considered to be magnetized and inertial, while the small particles (i.e., electrons and positrons) are taken to obey the Fermi–Dirac statistics. The well-known reductive perturbation analysis is applied to obtain the nonlinear Zakharov–Kuznetsov–Burgers equation (NZKBE). The analytical shock wave solution is obtained by employing the tanh technique. Furthermore, the asymptotic behavior and the stability of the shock structures are discussed. In the current model, the disturbances of nonlinear isothermal ion acoustic waves are found to exhibit only monotonic IIASWs. The consequences of the chemical potential, the presence of ultra-relativistic degenerate electrons and positrons, and magnetic field on the essential properties of three-dimensional IIASWs are numerically examined. The numerical investigations give rise to significant high lights on the propagation and the dynamic behavior of IIASWs. It is found that the amplitudes of the monotonic IIASWs decrease with chemical potentials of ultra-relativistic degenerate electrons and positrons increase.