In recent decades, plastic waste management has become one of the main environmental challenges for today’s society. The excessive consumption of so-called single-use plastics causes continuous damage to ecosystems, and it is necessary to find alternatives to recycle these products. In this work, a mechanical and hygrothermal characterisation of novel plaster composites incorporating LDPE waste in their interior was carried out. Thus, prefabricated plasterboards have been designed with a partial replacement of the original raw material with recycled LDPE in percentages of 5–10–15% by volume. The results show how these new composites exceeded the 0.18 kN minimum breaking load in panels in all cases, while decreases in density and thermal conductivity of up to 15% and 21%, respectively, were obtained. In addition, an increase of 3.8%in thermal resistance was obtained by incorporating these new gypsum boards in lightweight façade walls through simulations. In this way, a new pathway was explored for the recovery of these wastes and their subsequent application in the construction sector.