In this paper, we consider a distributed stochastic computation of AXB=C with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of AXB=C, we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm. Moreover, a numerical example is also given to illustrate the effectiveness of the proposed algorithm.