Deployable sunscreens with tensegrity architecture have been recently proposed for dynamic solar façades of buildings working on low energy consumption. Such structures are aimed at ensuring well-being indoor conditions while using reduced electrical-grid energy. The present paper studies the dynamical response of the tensegrity shading screens recently appeared in the literature, by studying structures formed by modular panels suitably assembled to form an origami pattern. The origami tensegrity façade is activated by stretching or releasing selected cables. Its energy-harvesting ability arises from the action of piezoelectric effects under the opening/closure motion of the origami panels, and wind-induced fluctuations. The dynamic response of the origami panels is simulated through a fully tensegrity model, with the aim of estimating their energy harvesting ability. The given results show that the overall tensegrity façade can daily produce a quantity of electric energy equivalent to the electric power produced by more than 200 squared meters of photovoltaic panels, and about 90 squared meters of rooftop wind turbines.