Shock-waves have historically been modeled assuming ideal gas behavior, yielding universal jump relations and a viscous structure that depends almost exclusively on the Mach number. However, many fluids of physical interest operate in dense or supercritical regimes where ideal gas thermodynamics no longer applies. Therefore, this work investigates the structure of shock-waves at supercritical fluid conditions without invoking ideal gas assumptions. Starting from the Navier–Stokes equations coupled with a real fluid thermophysical model, the governing relations are derived for the spatial evolution of thermodynamic variables across the shock. Using supercritical carbon dioxide as a representative fluid, it is shown that non-ideal thermodynamics strongly modifies the pressure–density jump relations and internal profiles of shocks, producing substantial deviations from classical Rankine-Hugoniot predictions. Interestingly, despite these pronounced thermodynamic effects, the physical thickness of the shock remains primarily controlled by the upstream Mach number. Taking both the structural and thermodynamic observations together, these results ultimately reveal how non-ideal fluid behavior fundamentally alters compressive discontinuities, thereby establishing the strict limits of classical shock theory in dense and supercritical fluids.