The problem of acoustic wave propagation in an auxetic (i.e., having a negative Poisson’s ratio) metamaterial is considered as self-consistent, including, along with the dynamic equations of a deformable solid, a kinetic equation for the density of defects. When formulating the problem, it is assumed that the main processes determining the behavior of defects are the processes of generation, recombination and diffusion. The dispersion equation of the system under consideration contains complex coefficients, from which it follows that the wave will not only propagate in the medium, but also attenuate as it propagates. The influence of the types of point defects (vacancies, interstitials), as well as the auxeticity of the material on the nature of dispersion (normal or anomalous), nonlinearity and frequency dependence of wave attenuation is revealed.