Integrating a solar water heater (SWH) with a phase change material (PCM)-based latent heat storage is an attractive method for transferring load from peak to off-peak hours. This transferring load varies as the physical parameters of the PCM change. Thus, the aim of this study is to perform a parametric analysis of the SWH on the basis of the PCM’s thermophysical properties. A mathematical model was established, and a computation code was developed to describe the physical phenomenon of heat storage/release in/from the SWH system. The thermal energy stored and the energy efficiency are used as key performance indicators of the new SWH–PCM system. The obtained numerical results demonstrate that the used key performance indicators were significantly impacted by the PCM thermo-physical properties (melting temperature, density, and latent heat). Using this model, various numerical simulations are performed, and the results indicate that, SWH with PCM, 20.2% of thermal energy on-peak periods load is shifted to the off-peak period. In addition, by increasing the PCM’s density and enthalpy, higher load shifting is observed. In addition, the PCM, which has a lower melting point, can help the SWH retain water temperature for a longer period of time. There are optimal PCM thermo-physical properties that give the best specific energy recovery and thermal efficiency of the SWH–PCM system. For the proposed SWH–PCM system, the optimal PCM thermo-physical properties, i.e., the melting temperature is 313 K, the density is 3200 kg/m3, and the latent heat is 520 kg/kg.