Micro- and nanotexturization of surfaces can give to the parts different advanced functionalities, such as superhydrophobicity, self-cleaning, or antibacterial capabilities. These advanced properties in combination with the biocompatibility of Liquid Silicone Rubber are an interesting approach for obtaining high-performance medical devices. The industrial production of surface textures in polymeric materials is through the replication technique, and the best option to attain a high production rate is injection molding. Moreover, its low viscosity during processing can provide an accurate replication capacity by the easy filling by capillarity of the microtextures. An innovative replicating technique for Liquid Silicone Rubber is presented by studying the replication of different shaped textures within a diameter range of between 2 and 50 µm. The copying process consists in the overmolding of a textured polymeric inlay obtained by nanoimprint lithography. At the end of the process, a textured part is obtained, while the imprinted film remains in the mold. The injection molding parameters are optimized to increase the replication accuracy, and their effect on texture replicability is analyzed and discussed. Finally, it is shown that the textured surfaces improve their wettability behavior, which is a necessary and important characteristic in the development of biomedical devices.