The lack of modern electricity supply has been a major impediment to proper functioning of the healthcare centers in the rural areas, contributing to high maternal and child mortality rates in a country. Therefore, this study focuses on how to address the identified problem so that the healthcare centers or clinics in the remote areas can provide timely delivery of medical services for the concerned people. This paper, then, presents the analysis of stand-alone hybrid renewable energy systems for basic healthcare services in the rural areas, where there is no grid energy supply or the supply from the existing grid is erratic and unreliable. One major factor that informs the selection of the hybrid energy system in this study is that it promises high reliability compared to a single energy system. The research presents a statistical analysis of the potential of wind and solar energies for a selected rural locations in Nigeria based on the available long-term hourly and daily meteorological data. It employs an optimal technical and economic design and sizing of hybrid electrical power systems' components such as the wind, PV, battery and inverter systems, using the hybrid optimisation software (HOMER). Results show that Sokoto and Jos sites exist in the high wind potential regions, while the remaining sites are only suitable for small wind applications. Values obtained for global radiation show that all the sites enjoy considerable solar energy potential suitable for varying degree of solar energy applications. PV/wind/diesel/battery hybrid system configuration is considered optimum for rural health center at Iseyin, Sokoto, Maiduguri, Jos and Enugu, while hybrid systems involving PV/diesel/battery is considered ideal for Port-Harcourt, due to the quality of renewable energy potential. Hence, it was concluded that, the abundance of wind and solar resources in the country create an ideal environment for inclusion of renewable energy systems in the design and implementation of standalone power supply systems to improve rural healthcare delivery.