This paper studies the problem of recovering an arbitrarily distributed sparse matrix from its one-bit (1-bit) compressive measurements. We propose a matrix sketching based binary method iterative hard thresholding (MSBIHT) algorithm by combining the two dimensional version of BIHT (2DBIHT) and the matrix sketching method, to solve the sparse matrix recovery problem in matrix form. In contrast to traditional one-dimensional BIHT (BIHT), the proposed algorithm can reduce computational complexity. Besides, the MSBIHT can also improve the recovery performance comparing to the 2DBIHT method. A brief theoretical analysis and numerical experiments show the proposed algorithm outperforms traditional ones.