In this paper, we propose a novel sparse source separation method that can be applied even if the number of sources is unknown. Recently, many sparse source separation approaches with time-frequency masks have been proposed. However, most of these approaches require information on the number of sources in advance. In our proposed method, we model the histogram of the estimated direction of arrival (DOA) with a Gaussian mixture model (GMM) with a Dirichlet prior. Then we estimate the model parameters by using the maximum a posteriori estimation based on the EM algorithm. In order to avoid one cluster being modeled by two or more Gaussians, we utilize a sparse distribution modeled by the Dirichlet distributions as the prior of the GMM mixture weight. By using this prior, without any specific model selection process, our proposed method can estimate the number of sources and time-frequency masks simultaneously. Experimental results show the performance of our proposed method.