Photocatalytic activity of semiconductor nanostructures is gaining much importance in recent years in both energy and environmental applications. However, several parameters play a crucial role in enhancing or suppressing the photocatalytic activity through, for example, modifying the band gap energy positions, influencing the generation and transport of charge carriers and altering the recombination rate. In this regard, physical parameters such as the support material and the irradiation source can also have significant effect on the activity of the photocatalysts. In this work, we have investigated the role of reduced graphene oxide (RGO) support and the irradiation source on mixed metal chalcogenide semiconductor (CdS–ZnO) nanostructures. The photocatalyst material was synthesized using a facile hydrothermal method and thoroughly characterized using different spectroscopic and microscopic techniques. The photocatalytic activity was evaluated by studying the degradation of a model dye (methyl orange, MO) under visible light (only) irradiation and under natural sunlight. The results reveal that the RGO-supported CdS–ZnO photocatalyst performs considerably better than the unsupported CdS–ZnO nanostructures. In addition, both the catalysts perform significantly better under natural sunlight than under visible light (only) irradiation. In essence, this work paves way for tailoring the photocatalytic activity of semiconductor nanostructures.