A dynamic development in building-integrated photovoltaics (BIPVs) has been observed in recent years. One of the manifestations of this trend is the integration of photovoltaic cells with tensile membrane structures, including canopies. Such solutions bring mutual benefits—the roofs provide a potentially large area for the application of photovoltaic cells while contributing to the improvement of the energy efficiency of the building. However, what is lacking is thorough research on the most favourable photovoltaic cell exposure within these roofs. This paper investigates the optimal position of photovoltaic cells in terms of energy gains related to exposure to solar radiation. Hypar geometries were simulated as the most characteristic of tensile membrane roofs and, simultaneously, the least obvious in the research context. Simulations were performed for 54 roof samples with the following geometric variables: roof height (1.0, 3.0 m) and membrane prestress (1:3, 1:1, 3:1). The research was conducted for three roof orientations defined by azimuth angles of 0, 22.5, and 45 degrees and three geographic locations, Oslo, Vienna, and Lisbon, representing Northern, Central, and Southern Europe, respectively. The Sofistik and Rhino + Ladybug software were used to create models and simulations. The study results show significant differences in the roof irradiation and, consequently, the optimal location of BIPVs depending on the above variables. Generally, it is the curvature that is the most important variable-less curved roofs are more irradiated and thus more suitable for BIPVs. Prestress and the azimuth angle are of lesser significance, but defining the optimal use of a BIPV depends on the adopted scenario regarding the percentage of membrane coverage with PVs—other recommendations concern the strategy of total or partial roof coverage with PV cells. The difference between optimally and incorrectly designed roofs may amount to a 50% electricity gain from PV cells.