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.