This paper introduces a novel Bayesian framework for probabilistic clustering of matrix-valued data. The proposed approach models the number of clusters as a stochastic partition of the data and introduces a sparsity constraint on the covariance matrices using a beta shrinkage prior for the off-diagonal elements. The effectiveness and superiority of the proposed MCMC algorithm are demonstrated through simulation studies, showing improved estimation of group structures compared to competing methods. It is further tested on two data applications including adrenal lesion clustering and household energy use, aiming to uncover potential disease subtypes and user profile subpopulations.