Nowadays, the need to reduce the dependence on fuel products and to achieve a sustainable development is of special importance due to environmental concerns. Therefore, new alternatives must be sought. In this work, extruded fibers from poly (lactic acid) (PLA) and poly (butylene adipate-co-terephthalate) (PBAT) added with cinnamon essential oil (CEO) were prepared and characterized, and the hydrolytic degradation was assessed. A two-phase system was observed with spherical particles of PBAT embedded in the PLA matrix. The thermal analysis showed partial miscibility between PLA and PBAT. Mechanically, Young’s modulus decreased and the elongation at break increased with the incorporation of PBAT and CEO into the blends. The variation in weight loss for the fibers was below 5% during the period of hydrolytic degradation studied with the most important changes at 37 °C and pH 8.50. From microscopy, the formation of cracks in the fiber surface was evidenced, especially for PLA fibers in alkaline medium at 37 °C. This study shows the importance of the variables that influence the performance of polyester-cinnamon essential oil-based fibers in agro-industrial applications for horticultural product preservation.