The European Green Deal establishes the efficient management of construction resources as one of its main lines of action. In this sense, the recovery of construction and demolition waste for its reincorporation into the manufacturing process of new sustainable materials has become necessary for the industry. This work deals with the physical and mechanical characterization of cement mortars made with recycled concrete aggregates and reinforced with natural fibers. The reinforcement fibers used (abaca, coconut, and toquilla) are more environmentally friendly compared to traditional synthetic reinforcements. The aim of this research is to analyze the main physico-mechanical properties of these sustainable cement mortars. The results show that mortars made with recycled sand have a lower density and better thermal performance than traditional mortars. In addition, with the incorporation of these natural fibers, the flexural strength of the mortars with recycled aggregate increased by up to 37.6%. Another advantage obtained from the incorporation of these natural fibers is the reduction in shrinkage in the masonry mortars during the drying process, giving them greater dimensional stability and making their behavior similar to that of traditional mortars. Thus, this work shows the potential application of masonry mortars produced under circular economy criteria and their application in the building sector.