Abstract: To address the bottlenecks of traditional sound-absorbing structures—namely, the narrow effective frequency band in low-frequency noise control and the difficulty in balancing load-bearing capacity with acoustic performance—a self-locking acoustic metamaterial structure composed of nested circular rings exhibiting a negative Poisson’s ratio is proposed. Based on acoustic wave theory, the wave equation for sound propagation is derived, and the cutoff frequency is determined. A finite-element acoustic model is established to analyze the auxetic behavior and acoustic performance of the structure, and the reliability of the simulation is verified through impedance-tube experiments. The results show that the structure achieves effective sound absorption (absorption coefficient > 0.5) in the frequency ranges of 292–731 Hz and 1356–1527 Hz, with peak values of 0.86 at 440 Hz and 0.60 at 1440 Hz. Its acoustic performance can be further improved by optimizing the porous material and the geometric parameters of the cylindrical shells. After integrating acoustic black holes, the sound absorption performance is significantly enhanced across a broad frequency band of 50–1600 Hz. The structure maintains cavity stability via a self-locking mechanism and synergistically combines the advantages of Helmholtz resonators, acoustic black holes, and auxetic configurations, offering a novel solution for broadband noise control with enhanced load-bearing stability.