Unwanted mechanical vibrations at low frequencies, particularly in sensitive systems with space constraints, constitute one of the major challenges in vibration engineering. In this study, a vibration isolator exhibiting quasi-zero-stiffness (QZS) behavior is designed and analyzed. The proposed unit cell consists of a positive-stiffness element based on an eye-shaped geometry combined with initially curved beams acting as negative-stiffness elements. Unlike many conventional multi-component configurations, this integrated design is developed to reduce the required installation space while enabling adjustment of the mechanical response through variations in geometric parameters. Nonlinear static analysis performed in COMSOL shows that this geometric combination creates a region of near-zero effective stiffness in the vicinity of the equilibrium point. Furthermore, numerical investigation of the system’s dynamic response indicates a significant reduction in vibration transmission within the low-frequency range. The numerical results demonstrate that the proposed structure, while maintaining static stability, provides tunable isolation performance through variations in geometric parameters and can therefore be considered a suitable option for applications with limited installation space.