With the extensive application of acoustic metamaterial (AM) in the mechanical industry, the crack detection of AM becomes increasingly crucial. In this paper, a weighted mode shape-wavelet-based strategy coupled with edge-based smoothed finite element (ES-FEM) is presented for damage detection of AM. Firstly, the multi-order mode shapes of cracked AM are computed by ES-FEM, and the obtained mode shape data is further interpolated and extended. Then, the multi-order detail coefficients of smoothed mode shapes are calculated through the discrete wavelet transform (DWT). Finally, the damage index and crack width estimator are established from the weighted multi-order detail coefficients to locate the crack and predict crack width, respectively. Numerical results demonstrate that the traditional modal-wavelet based crack detection strategy is very ambiguous while the proposed ES-FEM coupled weighted crack detection strategy is very effective for crack location and crack size prediction of AM.