In this paper, we study the role of sparsity and intra-vector correlation in the problem of multiuser multiple-input multiple-output millimeter wave channel estimation. In order to estimate the channel, we formulate a hierarchical zero mean correlated Gaussian prior with covariance matrix that can incorporate known correlation models while at the same time inducing spatial sparsity. For this prior, we develop a Bayesian algorithm based on evidence maximization to recover the correlated sparse vector. The solution to the hyperparameter update in the resulting algorithm is obtained as a fixed-point iteration. We empirically evaluate the proposed algorithm in terms of the normalized mean squared error in channel estimation under orthogonal pilots, and compare it against genie-aided estimators and standard sparse recovery methods. The results demonstrate that exploiting correlation can provide significant performance gains, even with imperfect channel covariance information.