In this work, we consider the estimation of multiple jointly sparse vectors (or signals) from noisy, undetermined, linear measurements acquired by multiple nodes connected in a network. We propose a decentralized Bayesian algorithm, which is able to exploit the joint sparsity structure across the nodes. In the proposed algorithm, each node seeks the maximum a posterior probability (MAP) estimate of a local sparse signal vector by learning the parameters of a sparsity inducing signal prior, which is assumed to be common to the nodes, in a distributed fashion. Through simulations, we show that our algorithm significantly outperforms DCS-SOMP, an existing algorithm, in terms of number of measurements required per node for exact recovery of the common support. We also propose a tuning procedure to accelerate the convergence of our algorithm.