Achieving a balance between low-frequency bandgaps and high load capacity is a critical challenge in metamaterial design. Leveraging the post-buckling behavior of bars, this study proposes a novel tensegrity metamaterial where post-buckling induces a reduction in structural stiffness, thereby enabling low-frequency vibration isolation while enhancing load-bearing capacity. The elliptic integral method is employed to rapidly compute post-buckling deformations and determine the stiffness of the tensegrity unit. Bandgap frequencies are calculated using Bloch’s theorem under periodic boundary conditions, combined with a spring-mass diatomic chain model. To optimize both band gap and load capacity, a data-driven, dual-objective optimization method is employed, yielding the Pareto frontier for the metamaterial’s ultimate load and lower bandgap limit. The results demonstrate that the optimized structure can achieve bandgap frequency as low as 3 Hz, with a load capacity exceeding 100 N. Compared to existing low-frequency vibration isolation metamaterials, the ultimate load capacity is increased by over 3.6 times at the same bandgap frequency.