The present study investigates the incorporation of renewable rooftop photovoltaic systems in fully electrified residential buildings and estimates the zero-energy demand building potential in relation to the climatic data of Greece. Specifically, the aim of the analysis is to calculate the maximum possible number of stories and therefore the total building height for a complete transformation to zero-net-energy building. The energy analysis, which is conducted using the DesignBuilder software, focuses on single-floor up to seven-story buildings. The importance of the present work lies in the acknowledgment of the diversity of the Greek residential sector, the adherence to national energy policies, and the European goal of fully electrified buildings. The examined case studies are equipped with electrically driven air-to-air heat pumps serving the space heating and cooling demands and with an air-to-water heat pump covering the domestic hot water requirements. The investigated locations are the four main cities of Greece, Athens, Thessaloniki, Chania, and Kastoria, which represent the country’s four climatic categories. The conducted analysis allows for the mapping of the zero-energy building potential for the climatic data of Greece, demonstrating the possibility of striking a positive building energy balance through the integration of on-site renewable energy sources and the production of necessary electrical energy. The novelty of the present work lies in the identification of a key factor, namely, the building height, which determines the feasibility of transforming multifamily buildings into zero-energy buildings. According to the analysis results, the critical number of stories is calculated at six for Chania, five for Athens, four for Thessaloniki, and two for Kastoria. Regarding a three-story residential building, the incorporation of a renewable photovoltaic system can result in an annual surplus electricity production of 13,741 kWh (Chania), 10,424 kWh (Athens), and 6931 kWh (Thessaloniki), and a corresponding coverage of 100% (Chania), 69.0% (Athens), 38.9% (Thessaloniki) and 0% (Kastoria).