Automobile vibrations increase noise levels and potential mechanical damage that hampers ride comfort. Engine mounts play a crucial role in maintaining the vehicles’ stability, performance, and convenience by securely supporting the engine and reducing the transmission of vibrations. Typical vibration dampeners are made of viscoelastic materials such as rubber or viscous fluid to absorb the energy. They need periodic maintenance as either rubber age with time or need refilling of viscous liquid. This research explored the possibility of using more reliable structures, such as auxetic materials, for vibration isolation in the above-mentioned practical applications. Using auxetic structures for manufacturing engine mounts in automobiles offers promising capabilities for vibration attenuation and enhanced damping. While metallic auxetic structures are predominantly used in practical applications, this study focuses on analyzing the behavior of polylactic acid (PLA) material to understand the behavior of auxetic structures. Experiments have been carried out on 3D-printed auxetic structures, and the vibration amplitude is noted at both the excitation and tip ends. The experimental data was used to build a machine learning model to design the auxetic structure that can provide the best vibration attenuation for a given frequency value in the given range of length and thickness. Then, a finite element analysis (FEM) on the auxetic structures was done using COMSOL Multiphysics software, and the FEM results were validated with the experimental data.